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FOUR-PLACE 

LOGARITHMIC 

AND 

TRIGONOMETRIC 
TABLES 


TOGETHER   WITH 


INTEREST  TABLES 


EDITED   BY 


LOUIS  C.  KARPINSKI 

ASSOCIATE   PROFESSOR  OF    MATHEMATICS 
UNIVERSITY   OF   MICHIGAN 


George  Wahr,  Publisher 
Ann  Arbor,  Michigan 


FOUR-PLACE 

LOGARITHMIC 

AND 

TRIGONOMETRIC 
TABLES 


TOGETHER   WITH 


INTEREST  TABLES 


EDITED   BY 


LOUIS  c.\karpinski 

ASSOCIATE  PROFESSOR  OF   MATHEMATICS 
UNIVERSITY   OF    MICHIGAN 


George  Wahr,  Publisher 
Ann  Arbor,  Michigan 


CAJORl 

Copyright^  191 8 

BY 

Louis  C.  Karpinski 
All  rights  reserved 


Ann  Arbor  PrKss 
ann  arbor^  mich. 


QA55 

^3 


CONTENTS 


Explanation  of  the  tables 5-7 

I.     Constants  with  their  logarithms 9 

II.     Logarithms  of  numbers,   100-999 lo-ii 

III.  Logarithms  of  numbers,   1000-2009 12-13 

IV.  Logarithms  of  sines  and  cosines,  10'  intervals.  14-15 
V.     Logarithms  of  tangents  and  cotangents, 

10'  intervals 16-17 

VI.     Logarithms  of  sines  and  tangents  by  minutes, 

0°  to  14° 18-19 

Logarithms  of  cosines  and  cotangents  by  min- 
utes, 76°  to  90°. 
VII.     Numerical  values  of  sines  and  cosines, 

10'  intervals 20-21 

VIII.     Numerical  values  of  tangents  and  cotangents, 

10'  intervals    22-23 

IX.     Squares,  cubes,  square-roots,  cube-roots,  and 

reciprocals,  i  to  100 24 

X.     Degrees  and  minutes  expressed  in  radians ....       25 

Values  of  e''  and  e"'^. 
XL     Accumulation  of  i  at  the  end  of  n  years,  r«.  . .       26 
XII.     The  present  value  of  i  in  n  years,  z^" 27 

XIII.  The  accumulation  of  an  annuity  of  i  per 

annum  at  the  end  of  n  years .  .  . , 28 

XIV.  The  present  value  of  an  annuity  of  i  per 

annum  for  n  years 29 

XV.     The  annual  sinking  fund  to  accumulate  to  i  at 

the  end  of  n  years 30 

By  addition  of  i  the  annuity  which  i  will 
purchase. 

—  3  — 


K 


Digitized  by  tine  Internet  Arcinive 

in  2007  witin  funding  from 

IVIicrosoft  Corporation 


littp://www.arcliive.org/details/fourplacelogaritOOkarpricli 


EXPLANATION  OF  THE  TABLES 

I,  General.  These  tables  are  arranged  to  give  maxi- 
mum speed  in  computing  which  falls  within  the  range  of  the 
tables.  F.or  engineers,  physicists,  chemists,  surveyors,  and 
for  statistical  experts  the  tables  will  be  found  to  be  adequate 
for  90%  to  99%  of  ordinary  work.  For  students  of  science 
and  mathematics  these  tables  make  possible  a  far  greater 
amount  of  drill  in  actual  computation  than  with  five-place 
tables;  the  use  of  the  four-place  table  emphasizes  the  fact 
that  computation  should  not  be  carried  beyond  the  places  to 
which  measurement  is  made,  and  this  is. rarely  to  more  than 
four  significant  figures. 

Certain  distinct  innovations  in  these  tables  are  to  be 
noted.  In  the  first  place  both  horizontal  and  vertical  inter- 
polation forms  are  given  in  order  to  afford  the  variety  of 
experience  which  will  be  of  service  when  further  and  more 
extensive  tables  are  used.  In  the  second  place  no  lines  are 
used  to  separate  the  columns  as  it  is  the  experience  of  com- 
puters that  the  lines  which  are  commonly  found  in  tables 
retard  the  speed  of  computation,  affecting  the  eye  unpleas- 
antly. In  the  third  place  the  entry  headings,  in  bold-face 
type,  are  repeated  in  the  middle  of  the  tables  to  reduce  to  a 
minimum  the  necessary  movement  of  the  eyes  and  to  elim- 
inate any  uncertainty  as  to  column  order,  thus  increasing 
both  speed  and  accuracy. 


2,  Particular. 

TABLE  II 

Mechanical  interpolation,  in  horizontal  form,  is 
introduced.  In  reading  the  logarithm  of  a  number  re- 
quiring interpolation,  like  232.4,  the  logarithm  of  232  is  read 

—  5  — 


EXPLANATION  OF  THE  TABLES 

as  2.3655  and  to  this  7,  the  4/10  of  the  tabular  difference,  is 
added  mentally,  noting  the  7  in  column  4  of  the  difference 
table.  In  writing  this  logarithm  2.36  is  written  immediately 
when  read ;  55  is  noted  mentally ;  a  glance  to  the  right,  col- 
umn 4,  shows  that  7  is  to  be  added,  giving  62 ;  then  2.36  is 
completed  to  2.3662,  the  required  logarithm.  An  error  of 
one  unit  in  the  last  place  is  possible,  but  that  is  equally  true 
with  ordinary  interpolation.  Mean  tabular  differences  are 
given. 

For  numbers  between  1000  and  2009  it  is  desirable  to 
use  the  special  table,  TABLE  III,  as  errors  of  one  to  two 
units  of  the  last  place  are  common  in  this  interval  when  the 
horizontal  scheme  of  interpolation  is  used. 

TABLE  IV  AND  TABLE  V 

Mean  differences  are  given  and  the  mechanical  scheme 
of  horizontal  interpolation  is  to  be  employed  as  in  TABLE 
II.  However  where  the  tabular  difference  is  10  or  less  inter- 
polation is  to  be  effected  by  noting  the  difference  and  using 
the  multiphcation  table. 

Thus,  log  sin  32°  2.(i'  is  obtained  by  writing  first,  9.72, 
noting  82  mentally ;  then  12  from  column  6  is  added  to  82, 
making  94;  finally  9.7294  is  written  as  the  required  log- 
arithm. 

log  cos  32°  26'  is  obtained  by  writing  9.92,  noting  68 
mentally;  the  tabular  difference,  a  decrease,  is  noted  as  8; 
then  6/10  of  8  is  obtained  mentally  as  5,  since  6x8  =  48 
giving  here  4.8  or  5 ;  finally  63  is  written,  giving  9.9263  as 
the  required  logarithm. 

Table  IV  differs  from  Table  V  in  that  the  given  tabu- 
lar difference  does  not  apply  to  the  double  line.  In  the 
lower  one  of  each  pair  of  lines,  the  interpolation  is  to  be 
performed  mentally,  except  in  the  last  twelve  lines  where 
both  tabular  differences  are  given. 

—  6  — 


EXPLANATION  OF  THE  TABLES 

TABLE  VI 

This  table  can  be  used  for  logarithms  of  cotangents 
between  o°  and  14°,  and  for  logarithms  of  tangents  be- 
tween 76°  and  90°,  both  by  minutes,  by  writing  the  comple- 
ment to  10  of  the  logarithm  of  the  given  tangent  or  cotan- 
gent. Thus  log  cot  4°  15'  is  obtained  by  noting  8.8699  in 
the  table,  and  writing  1.1301  as  log  cot  4°  15'.  This  same 
value  would  be  obtained,  in  a  similar  manner,  for  log  tan 
85°  45'. 

TABLE  VII  AND  TABLE  VIII 

Vertical  interpolation  is  introduced.  Thus,  sin  32°  26' 
is  obtained  by  writing  first  .53,  noting  48  mentally  and  noting 
at  the  right  the  mean  tabular  difference,  24;  then  6/10  of 
this  difference  is  read  as  14,  which  added  to  48  gives  62; 
finally,  .5362  is  the  required  value.  The  correct  four-place 
value  is  .5363,  and  this  would  have  been  obtained  by  using 
the  actual  tabular  difference,  25  (.0025),  between  .5348  and 

•5373- 

Were  .5362  given  as  the  sine  of  an  angle  the  angle 
would  be  obtained  by  noting  that  .5348  is  sin  32°  20' ;  the 
tabular  difference  of  24  is  noted,  and  the  actual  difference  of 
14  units  of  the  last  place  is  found  to  be  nearest  to  6/10  of 
24,  giving  32°  26'  as  the  angle.  Were  25,  the  real  and  not 
the  mean  tabular  difference  used,  the  14  would  be  mid-way 
between  5/10  and  6/10  of  the  difference;  in  this  event  com- 
puters make  it  a  rule  to  take  the  even  digit,  giving  here  again 
32°  26'. 


—  7 


TABLE  I 


CONSTANTS  WITH  THEIR  LOGARITHMS 

Base  of  natural  logarithms 
Modulus  of  common  logarithms 

Circumference  of  a  circle  in  degrees 
Circumference  of  a  circle  in  minutes 
Circumference  of  a  circle  in  seconds 

Radius  of  a  circle  in  degrees  or  1  radian 

Radius  of  a  circle  in  minutes 

Radius  of  a  circle  in  seconds 

Ratio  of  a  circumference  to  diameter 

Volumes  and  WETGHxa 

Cubic  inches  in  one  gallon  (U.  S.), 
Gallons  in  one  cubic  foot 
Cubic  inches  in  one  bushel 

Pounds  per  cubic  foot  of  water  (4  °  C) 
Pounds  per  cubic  foot  of  air  (0  °  C) 
Cubic  feet  in  one  cubic  meter 
Cubic  meters  in  one  cubic  yard 
Cubic  inches  in  one  liter 
Liters  in  one  gallon  (U.  S.) 

Pounds  in  one  kilogram  2.2  or 

Metric  ton  in  pounds 

Volume  of  sphere,    =4.1888r3 

Acceleration  gravity,  g,  at  sea  level,  New  York, 

cm.  sec.  system 
Acceleration  gravity,  g,  at  sea  level,  New  York, 

ft.  sec.  system 

Lengths  and  Areas 

Inches  in  one  meter  (By  Act  of  Congress) 
Feet  in  1  rod,  16.5;  yds.  in  1  rod,  5.5 
Square  feet  in  one  acre 

160  SQUARE  R0DS  =  1  ACRE;   640  ACRES = 

3 .281  FEET  =  1 .094  YDS.  =1  METER. 

1  HORSE  POWER  =33,000  FT  .-LB.  Per  Min.=550  FT.-LB.  Per  Sec. 

1    KILOWATT  =1.341  HORSEPOWER  =737.5  FT.-LB.  Per  Second 

1  CUBIC  FOOT  Per  Sec.  =448 .9  GAL  .Per  Min.  =1 .9835  ACRE-FT.  Per 

1  ACRE-FT.  Per  Day  =5.042  CU.  FT.  Per  Sec. 

1  BTU.  =778.4  FT.-LB.  =252  KG.-CAL. 

1  REV.  Per  Min.  =6  Per  Sec.  =  .2832  RADIANS  Per  Min. 

1  FT.  Per  Sec.  =  .6818  MILES  Per  Hour. 
LOGelO  =2. 302585,  LOGioE  =  .434234. 


Number 
2.71828183 
0.43429448 

Logarithm 
0.4342945 
9.6377843-10 

360 
21600 
1296000 

2.5563025 
4.3344538 
6.1126050 

57.29578 
3437.7468 
206264.806 

3.14159265 

1.7581226 
3.5362739 
5.3144251 
0.4971499 

231 
7.48 
2150.4 

2.3636 

.8739 

3.3325 

62.43 

.0807 
35.32 

.76 
61.03 
3.786 

1.7954 
8.9069-10 
1.5480 
9.8808-10 
1.7855 
.5782 

2.2046 
2205 

4 .  1888r3- 

.3434 

3.3434 

.6221 

980.2 

2.9913 

32.16 

1.5073 

39.37 

1.5952 

43560 

4.6391 

iQ.  MILE. 

Day. 


—  9  — 


TABLE  II 


LOGARITHMS  OF  NUMBERS:  100-549 


N       0         1         2         3  4         5 

13  0000  0043  0086  0128  0170  0212 

11  0414  0453  0492  0531  0569  0607 

12  0792  0828  0864  0899  0934  0969 

13  1139  1173  1206  1239  1271  1303 

14  1461  1492  1523  1553  1584  1614 


6         7         8         9       D1234567S9 

0253  0294  0334  0374  41  4  8  12  17  21  25  29  33  37 
0645  0682  0719  0755  38  4  8  11  15  19  23  26  30  34 
1004  1038  1072  1106  35  3  7  10  14  17  21  24  28  31 
1335  1367  1399  1430  32  3  6  10  13  16  19  23  26  29 
1644  1673  1703  1732  30  3  6  9  12  15  18  21  24  27 


15  1761  1790  1818  1847  1875  1903 

16  2041  2068  2095  2122  2148  2175 

17  2304  2330  2355  2380  2405  2430 

18  2553  2577  2601  2625  2648  2672 

19  2788  2810  2833  2856  2878  2900 

20  3010  3032  3054  3075  3096  3118 

21  3222  3243  3263  3284  3304  3324 

22  3424  3444  3464  3483  3502  3522 

23  3617  3636  3655  3674  3692  3711 

24  3802  3820  3838  3856  3874  3892 

25  3979  3997  4014  4031  4048  4065 

26  4150  4166  4183  4200  4216  4232 

27  4314  4330  4346  4362  4378  4393 

28  4472  4487  4502  4518  4533  4548 

29  4624  4639  4654  4669  4683  4698 


1931  1959  1987  2014  28  3  6 

2201  2227  2253  2279  27  3  5 

2455  2480  2504  2529  25  2  5 

2695  2718  2742  2765  24  2  5 

2923  2945  2967  2989  23  2  4 

3139  3160  3181  3201  22  2  4 

3345  3365  3385  3404  21  2  4 

3541  3560  3579  3598  20  2  4 

3729  3747  3766  3784  19  2  4 

3909  3927  3945  3962  18  2  4 

4082  4099  4116  4133  17  2  4 

4249  4265  4281  4298  16  2  3 

4409  4425  4440  4456  15  2  3 

4564  4579  4594  4609  15  2  3 

4713  4728  4742  4757  14  1  3 


8  11  14  17  20  22  25 
8  11  13  16  18  21  24 
7  10  12  15  17  20  22 
7  9  12  14  16  19  21 
7  9  11  13  16  18  20 

6  8  11  13  15  17  19 

6  8  10  12  14  16  18 

6  8  10  12  14  16  17 

6  7  9  11  13  15  17 

5  7  9  11  12  14  16 

5  7  9  10  12  14  16 

5  7  8  10  11  13  15 

5  6  8  9  11  12  14 

5  6  8  9  11  12  14 

4  6  7  9  10  12  13 


N 


9   D  1  2  3  4  5 


7  8 


30  4771  4786  4800  4814  4829  4843 

31  4914  4928  4942  4955  4969  4983 

32  5051  5065  5079  5092  5105  5119 

33  5185  5198  5211  5224  5237  5250 

34  5315  5328  5340  5353  5366  5378 


4857  4871  4886  4900  14  1  3 
4997  5011  5024  5038  13  1  3 
5132  5145  5139  5172  13  1  3 
5263  5276  5289  5302  13  1  3 
5391  5403  5416  5428  12  1  2 


4  6  7  9  10  11  13 

4  5  7  8  10  11  12 

4  5  7  8  9  11  12 

4  5  7  8  9  11  12 

4  5  6  7  9  10  11 


35  5441  5453  5465  5478  5490  5502 

36  5563  5575  5587  5599  5611  5623 

37  5682  5694  5705  5717  5729  5740 

38  5798  5809  5821  5832  5843  5855 

39  5911  5922  5933  5944  5955  5966 

40  6021  6031  6042  6053  6064  6075 

41  6128  6138  6149  6160  6170  6180 

42  6232  6243  6253  6263  6274  6284 

43  6335  6345  6355  6365  6375  6385 

44  6435  6444  6454  6464  6474  6484 


5514  5527  5539  5551  12  1  2 
5635  5647  5658  5670  12  1  2 
5752  5763  5775  5786  11  1  2 
5866  5877  5888  5899  11  1  2 
5977  5988  5999  6010  11  1  2 

6085  6096  6107  6117  11  1  2 

6191  6201  6212  6222  10  1  2 

6294  6304  6314  6325  10  1  2 

6395  6405  6415  6425  10  1  2 

6493  6503  6513  6522  10  1  2 


4  5  6  7  9  10  11 

4  5  6  7  8  10  11 

4  5  6  7  8  9  11 

4  5  6  7  8  9  10 

3  4  5  7  8  9  10 

3  4  5  6  8  9  10 

3  4  5  6  7  8  9 

3  4  5  6  7  8  9 

3  4  5  6  7  8  9 

3  4  5  6  7  8  9 


45  6532  6542  6551  6561  6571  6580 

46  6628  6637  6646  6656  6665  6675 

47  6721  6730  6739  6749  6758  6767 

48  6812  6821  6830  6839  6848  6857 

49  6902  6911  6920  6928  6937  6946 


6590  6599  6609  6618  10  1  2 
6684  6693  6702  6712  9  12 
6776  6785  6794  6803  9  1  2 
6866  6875  6884  6893  9  1  2 
6955  6964  6972  6981  9  1  2 


3  4  5  6  7  8  9 

3  4  5  6  7  7  8 

3  4  5  6  7  7  8 

3  4  5  6  7  7  8 

3  4  4  5  6  7  8 


50  6990  6998  7007  7016  7024  7033 

51  7076  7084  7093  7101  7110  7118 

52  7160  7168  7177  7185  7193  7202 

53  7243  7251  7259  7267  7275  7284 

54  7324  7332  7340  7348  7356  7364 
N   0    1   2    3  4    5 


7042  7050  7059  7067  9  1  2 

7126  7135  7143  7152  8  12 

7210  7218  7226  7235  8  1  2 

7292  7300  7308  7316  8  12 

7372  7380  7388  7396  8  1  2 

6    7    8    9  Dl 2 


3  4  4  5  6  7  8 

3  3  4  5  6  7  8 

3  3  4  5  6  7  7 

2  3  4  5  6  6  7 

2  3  4  5  6  6  7 

3  4  5  6  7  8  9 


TABLE  II 


N   0    1    2    3 

55  7404  7412  7419  7427 

56  7482  7490  7497  7500 

57  7559  7566  7574  7582 

58  7634  7642  7649  7657 

59  7709  7716  7723  7731 

60  7782  7789  7796  7803 

61  7853  7860  7868  7875 

62  7924  7931  7938  7945 

63  7993  8000  8007  8014 

64  8062  8069  8075  8082 

65  8129  8136  8142  8149 

66  8195  8202  8209  8215 

67  8261  8267  8274  8280 

68  8325  8331  8338  8344 

69  8388  8395  8401  8407 

70  8451  8457  8463  8470 

71  8513  8519  8525  8531 

72  8573  8579  8585  8591 

73  8633  8639  8645  8651 

74  8692  8698  8704  8710 


LOGARITHMS  OF  NUMBERS:  550-999 


N 


75  8751  8756  8762  8768 

76  8808  8814  8820  8825 

77  8865  8871  8876  8882 

78  8921  8927  8932  8938 

79  8976  8982  8987  8993 

80  9031  9036  9042  9047 

81  9085  9090  9096  9101 

82  9138  9143  9149  9154 

83  9191  9196  9201  9206 

84  9243  9248  9253  9258 

85  9294  9299  9304  9309 

86  9345  9350  9355  9360 

87  9395  9400  9405  9410 

88  9445  9450  9455  9460 

89  9494  9499  9504  9509 

90  9542  9.547  9552  9557 

91  9590  9595  9600  9605 

92  9638  9643  9647  9652 

93  96S5  9689  9694  9699 

94  9731  9736  9741  9745 

95  9777  9782  9786  9791 

96  9823  9827  9832  9836 

97  9868  9872  9877  9881 

98  9912  9917  9921  9926 

99  9956  9961  9965  9969 
N   0    1    2    3 


4    5 

6    7    8    9 

Dl  2 

3 

4 

5 

6 

7 

8 

9 

7435  7443 

7451  7459  7466  7474 

8  1  2 

2 

3 

4 

5 

5 

6 

7 

7513  7520 

7528  7536  7543  7551 

812 

2 

3 

4 

5 

5 

6 

7 

7589  7597 

7604  7612  7619  7627 

8  1  1 

2 

3 

4 

5 

5 

6 

7 

7664  7672 

7679  7686  7694  7701 

7  1  1 

2 

3 

4 

5 

6 

7 

7738  7745 

7752  7760  7767  7774 

7  1  1 

2 

3 

4 

5 

6 

7 

7810  7818 

7825  7832  7839  7846 

1  1  1 

2 

3 

4 

5 

6 

6 

7882  7889 

7896  7903  7910  7917 

7  1  1 

2 

3 

3 

5 

6 

6 

7952  7959 

7966  7973  7980  7987 

7  1  1 

2 

3 

3 

5 

5 

6 

8021  8028 

8035  8041  8048  8055 

7  1  1 

2 

3 

3 

5 

5 

6 

8089  8096 

8102  8109  8116  8122 

7  1  1 

2 

3 

3 

5 

5 

6 

8156  8162 

8169  8176  8182  8189 

71  1 

2 

3 

3 

5 

5 

6 

8222  8228 

8235  8241  8248  8254 

7  1  1 

2 

3 

3 

5 

5 

6 

8287  8293 

8299  8306  8312  8319 

6  1  1 

2 

3 

3 

5 

5 

6 

8351  8357 

8363  8370  8376  8382 

6  1  1 

2 

3 

3 

4 

5 

6 

8414  8420 

8426  8432  8439  8445 

6  1  1 

2 

3 

3 

4 

5 

6 

8476  8482 

8488  8494  8500  8506 

6  1  1 

2 

3 

3 

4 

5 

6 

8537  8543 

8549  8555  8561  8567 

6  1  1 

2 

3 

3 

4 

3 

6 

8597  8603 

8609  8615  8621  8627 

6  1  1 

2 

3 

3 

4 

5 

6 

8657  8663 

8669  8675  8681  8686 

6  1  1 

2 

2 

3 

4 

5 

5 

8716  8722 

8727  8733  8739  8745 

61  1 

2 

2 

3 

4 

0 

5 

4    5 

6   7    8    9 

D12 

3 

4 

5 

6 

7 

8 

9 

8774  8779 

8785  8791  8797  8802 

61  1 

2 

2 

3 

3 

4 

5 

5 

8831  8837 

8842  8848  8854  8859 

6  1  1 

2 

2 

3 

3 

4 

5 

8887  8893 

8899  8904  8910  8915 

6  1  1 

2 

2 

3 

3 

4 

5 

8943  8949 

8954  8960  8965  8971 

6  1  1 

2 

2 

3 

3 

4 

5 

8998  9004 

9009  9015  9020  9025 

5  1  1 

2 

2 

3 

3 

4 

5 

9053  9058 

9063  9069  9074  9079 

51  1 

2 

2 

3 

3 

4 

5 

9106  9112 

9117  9122  9128  9133 

5  1  1 

2 

2 

3 

3 

4 

5 

9159  9165 

9170  9175  9180  9186 

5  1  1 

2 

2 

3 

3 

4 

5 

9212  9217 

9222  9227  9232  9238 

5  1  1 

2 

2 

3 

3 

4 

5 

9263  9269 

9274  9279  9284  9289 

5  1  1 

2 

2 

3 

3 

4 

5 

9315  9320 

9325  9330  9335  9340 

5  1  1 

2 

2 

3 

3 

4 

5 

9365  9370 

9375  9380  9385  9390 

5  1  1 

2 

2 

3 

3 

4 

5 

9415  9420 

9425  9430  9435  9440 

5  1  1 

2 

2 

3 

3 

4 

5 

9465  9469 

9474  9479  9484  9489 

50  1 

2 

2 

3 

3 

4 

9513  9518 

9523  9528  9533  9538 

501 

2 

2 

3 

3 

4 

9562  9566 

9571  9576  9581  9586 

501 

2 

2 

3 

3 

4 

9609  9614 

9619  9624  9628  9633 

50  1 

2 

2 

3 

3 

4 

9657  9661 

9666  9671  9675  9680 

50  1 

2 

2 

3 

3 

4 

9703  9708 

9713  9717  9722  9727 

50  1 

2 

2 

3 

3 

4 

9750  9754 

9759  9763  9768  9773 

50  1 

2 

2 

3 

3 

4 

9795  9800 

9805  9809  9814  9818 

50  1 

2 

2 

3 

3 

4 

9841  9845 

9850  9854  9859  9863 

40  1 

2 

2 

3 

3 

4 

9886  9890 

9894  9899  9903  9908 

40  1 

2 

2 

3 

3 

4 

9930  9934 

9939  9943  9948  9952 

40  1 

2 

2 

3 

3 

3 

4 

9974  9978 

9983  9987  9991  9996 

40  1 

2 

2 

3 

3 

3 

4 

4    5 

6    7    8    9 

D  1  2 

3 

4 

5 

6 

7 

8 

9 

k 


TABLE  III 


L 

.OGAR 

ITHMS 

;  OF  NUMBERS:  1000-1509 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

100 

0000 

0004 

0009 

0013 

0017 

0022 

0026 

0030 

0035 

0039 

101 

0043 

0048 

0052 

0056 

0060 

0065 

0069 

0073 

0077 

0082 

102 

0086 

0090 

0095 

0099 

0103 

0107 

0111 

0116 

0120 

0124 

103 

0128 

0133 

0137 

0141 

0145 

0149 

0154 

0158 

1062 

0166 

104 

0170 

0175 

0179 

0183 

0187 

0191 

0195 

0199 

0204 

0208 

105 

0212 

0216 

0220 

0224 

0228 

0233 

0237 

0241 

0245 

0249 

106 

0253 

0257 

0261 

0265 

0269 

0273 

0278 

0282 

0286 

0290 

107 

0294 

0298 

0302 

0306 

0310 

0314 

0318 

0322 

0326 

0330 

108 

0334 

0338 

0342 

0346 

0350 

0354 

0358 

0362 

0366 

0370 

109 

0374 

0378 

0382 

0386 

0390 

0394 

0398 

0402 

0406 

0410 

110 

0414 

0418 

0422 

0426 

0430 

0434 

0438 

0441 

0445 

0449 

111 

0453 

0457 

0461 

0465 

0469 

0473 

0477 

0481 

0484 

0488 

112 

0492 

0496 

0500 

0504 

0508 

0512 

0515 

0519 

0523 

0527 

113 

0531 

0535 

0538 

0542 

0546 

0550 

0554 

0558 

0561 

0565 

114 

0569 

0573 

0577 

0580 

0584 

0588 

0592 

0596 

0599 

0603 

115 

0607  • 

0611 

0615 

0618 

0622 

0626 

0630 

0633 

0637 

0641 

116 

0645 

0648 

0652 

0656 

0660 

0663 

0667 

0671 

0674 

0678 

117 

0682 

0686 

0689 

0693 

0697 

0700 

0704 

0708 

0711 

0715 

118 

0719 

0722 

0726 

0730 

0734 

0737 

0741 

0745 

0748 

0752 

119 

0755. 

0759 

0763 

0766 

0770 

0774 

0777 

0781 

0785 

0788 

120 

0792 

0795 

0799 

0803 

0806 

0810 

0813 

0817 

0821 

0824 

121 

0828 

0831 

0835 

0839 

0842 

0846 

0849 

0853 

0856 

0860 

122 

0864 

0867 

0871 

0874 

0878 

0881 

0885 

0888 

0892 

0896 

123 

0899 

0903 

0906 

0910 

0913 

0917 

0920 

0924 

0927 

0931 

124 

0934 

0938 

0941 

0945 

0948 

0952 

0955 

0959 

0962 

0966 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

125 

0969 

0973 

0976 

0980 

0983 

0986 

0990 

0993 

0997 

1000 

126 

1004 

1007 

1011 

1014 

1017 

1021 

1024 

1028 

1031 

1035 

127 

1038 

1041 

1045 

1048 

1052 

1055 

1059 

1062 

1065 

1069 

128 

1072 

1075 

1079 

1082 

1086 

1089 

1092 

1096 

1099 

1103 

129 

1106 

1109 

1113 

1116 

1119 

1123 

1126 

1129 

1133 

1136 

130 

1139 

1143 

1146 

1149 

1153 

1156 

1159 

1163 

1166 

1169 

131 

1173 

1176 

1179 

1183 

1186 

1189 

1193 

1196 

1199 

1202 

132 

1206 

1209 

1212 

1216 

1219 

1222 

1225 

1229 

1232 

1235 

133 

1239 

1242 

1245 

1248 

1252 

1255 

1258 

1261 

1265 

126.S 

134 

1271 

1274 

1278 

1281 

1284 

1287 

1290 

1294 

1297 

1300 

135 

1303 

1307 

1310 

1313 

1316 

1319 

1323 

1326 

1329 

1332 

136 

1335 

1339 

1342 

1345 

1348 

1351 

1355 

1358 

1361 

1364 

137 

1367 

1370 

1374 

1377 

1380 

1383 

1386 

1389 

1392 

1396 

138 

1399 

1402 

1405 

1408 

1411 

1414. 

1418 

1421 

1424 

1427 

139 

1430 

1433 

1436 

1440 

1443 

1446 

1449 

1452 

1455 

1458 

140 

1461 

1464 

1467 

1471 

1474 

1477 

1480 

1483 

1486 

1489 

141 

1492 

1495 

1498 

1501 

1504 

1508 

1511 

1514 

1517 

1520 

142 

1523 

1526 

1529 

1532 

1535 

1538 

1541 

1544 

1547 

1550 

143 

1553 

1556 

1559 

1562 

1565 

1569 

1572 

1575 

1578 

1581 

144 

1584 

1587 

1590 

1593 

1596 

1599 

1602 

1605 

1608 

1611 

145 

1614 

1617 

1C20 

1623 

1626 

1629 

1632 

1635 

1638 

1641 

146 

1644 

1647 

1649 

1652 

1655 

1658 

1661 

1664 

1667 

1670 

147 

1673 

1676 

1679 

1682 

1685 

1688 

1691 

1694 

1697 

1700 

148 

1703 

1706 

1708 

1711 

1714 

1717 

1720 

1723 

1726 

1729 

149 

1732 

1735 

1738 

1741 

1744 

1746 

1749 

1752 

1755 

1758 

150 

1761 

1764 

1767 

1770 

1772 

1775 

1778 

1781 

1784 

1787 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

12    


TABLE  III 


LOGARITHMS  OF  NUMBERS:  1500-2009 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

150 

1761 

1764 

1767 

1770 

1772 

1775 

1778 

1781 

1784 

1787 

151 

1790 

1793 

-1796 

1798 

1801 

1804 

1S07 

1810 

1813 

1816 

152 

1818 

1821 

1824 

1827 

1830 

1833 

1836 

1838 

1841 

1844 

153 

1847 

1850 

1853 

1855 

1858 

1861 

1864 

1867 

1870 

1872 

154 

1875 

1878 

1881 

1884 

1886 

1889 

1892 

1895 

1898 

1901 

155 

1903 

1906 

1909 

1912 

1915 

1917 

1920 

1923 

1926 

1928 

156 

1931 

1934 

1937 

1940 

1942 

1945 

1948 

1951 

1953 

1956 

157 

1959 

1962 

1965 

1967 

1970 

1973 

1976 

1978 

1981 

1984 

158 

1987 

1989 

1992 

1995 

1998 

2000 

2003 

2006 

2009 

2011 

159 

2014 

2017 

2019 

2022 

2025 

2028 

2030 

2033 

2036 

2038 

160 

2041 

2044 

2047 

2049 

2052 

2055 

2057 

2060 

2063 

2066 

161 

2068 

2071 

2074 

2076 

2079 

2082 

2084 

2087 

2090 

2092 

162 

2095 

2098 

2101 

2103 

2106 

2109 

2111 

2114 

2117 

2119 

163 

2122 

2125 

2127 

2130 

2133 

2135 

2138 

2140 

2143 

2146 

164 

2148 

2151 

2154 

2156 

2159 

2162 

2164 

2167 

2170 

2172 

165 

2175 

2177 

2180 

2183 

2185 

2188 

2191 

2193 

2196 

2198 

166 

2201 

2204 

2206 

2209 

2212 

2214 

2217 

2219 

2222 

2225 

167 

2227 

2230 

2232 

2235 

2238 

2240 

2243 

2245 

2248 

2251 

168 

2253 

2256 

2258 

2261 

2263 

2266 

2269 

2271 

2274 

2276 

169 

2279 

2281 

2284 

2287 

2289 

2292 

2294 

2297 

2299 

2302 

170 

2304 

2307 

2310 

2312 

2315 

2317 

2320 

2322 

2325 

2327 

171 

2330 

?333 

2335 

2338 

2340 

2343 

2345 

2348 

2350 

2353 

172 

2355 

2358 

2360 

2363 

2365 

2368 

2370 

2373 

2375 

2378 

173 

2380 

2383 

2385 

2388 

2390 

2393 

2395 

2398 

2400 

2403 

174 

2405 

2408 

2410 

2413 

2415 

2418 

2420 

2423 

2425 

2428 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

175 

2430 

2433 

2435 

2438 

2440 

2443 

2445 

2448 

2450 

2453 

176 

2455 

2458 

2460 

2463 

2465 

2467 

2470 

2472 

2475 

2477 

177 

2480 

2482 

2485 

2487 

2490 

2492 

2494 

2497 

2499 

2502 

178 

2504 

2507 

2509 

2512 

2514 

2516 

2519 

2521 

2524 

2526 

179 

2529 

2531 

2533 

2536 

2538 

2541 

2543 

2545 

2548 

2550 

180 

2553 

2555 

2558 

2560 

2562 

2565 

2567 

2570 

2572 

2574 

181 

2577 

2579 

2582 

2584 

2586 

2589 

2591 

2594 

2596 

2598 

182 

2601 

2603 

2605 

2608 

2610 

2613 

2615 

2617 

^620 

2622 

183 

2625 

2627 

2629 

2632 

2634 

2636 

2639 

2641 

2643 

2646 

184 

2648 

2651 

?653 

2655 

2658 

2660 

2662 

2665 

2667 

2669 

185 

2672 

2674 

2676 

2679 

2681 

2683 

2686 

2688 

2690 

2693 

186 

2695 

2697 

2700 

2702 

2704 

2707 

2709 

2711 

2714 

2716 

187 

2718 

2721 

2723 

2725 

2728 

2730 

2732 

2735 

2737 

2739 

188 

2742 

2744 

2746 

2749 

2751 

2753 

2755 

2758 

2760 

2762 

189 

2765 

2767 

2769 

2772 

2774 

2776 

2778 

2781 

2783 

2785 

190 

2788 

2790 

2792 

2794 

2797 

2799 

2801 

2804 

2806 

2808 

191 

2810 

2813 

2815 

2817 

2819 

2822 

2824 

2826 

2828 

2831 

192 

2833 

2835 

2838 

2840 

2842 

2844 

2847 

2849 

2851 

2853 

193 

2856 

2858 

2860 

2862 

2865 

2867 

2869 

2871 

2874 

2876 

194 

2878 

2880 

2882 

2885 

2887 

2889 

2891 

2894 

2896 

2898 

195 

2900 

2903 

2905 

2907 

2909 

2911 

2914 

2916 

2918 

2920 

196 

2923 

2925 

2927 

2929 

2931 

2934 

2936 

2938 

2940 

2942 

197 

2945 

2947 

2949 

2951 

2953 

2956 

2958 

2960 

2962 

2964 

198 

2967 

2969 

2971 

2973 

2975 

2978 

2980 

2982 

2984 

2986 

199 

2989 

2991 

29?3 

2995 

2997 

2999 

3002 

3004 

3006 

3008 

200 

3010 

3012 

3015 

3017 

3019 

3021 

3023 

3025 

3028 

3030 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

—  13  — 


TABLE  IV 


A 

° 

0' 

0° 

sin 

'<[% 

cos 

sin 

8 

.2419' 

log 

cos 

9 

.9999 

2° 

sin 

8 

.5428 

log 

cos 

9 

.9997 

3° 

sin 

8 

.7188 

log 

cos 

9 

.9994 

4° 

sin 

8 

.8436 

log 

cos 

9 

.9989 

5° 

sin 

8 

.9403 

'7^ 

cos 

9 

.9983 

sin 

9 

.0192 

log 

cos 

9976 

7" 

sin 

0859 

log 

cos 

9968 

8° 

sin 

1436 

'7^ 

cos 

9958 

sin 

1943 

log 

cos 

9946 

10° 

sin 

9 

.2397 

log 

cos 

9 

.9934 

11° 

sin 

2806 

log 

cos 

9919 

A 

° 

0' 
60' 

12° 

sin 

3179 

log 

cos 

9904 

13° 

sin 

3521 

log 

cos 

9887 

14° 

sin 

3837 

log 

CCS 

9869 

15° 

sin 

4130 

log 

cos 

9849 

16° 

sin 

4403 

log 

cos 

9828 

17° 

sin 

4659 

log 

cos 

9806 

18° 

sin 

4900 

1-,^ 

cos 

9782 

sin 

5126 

log 

cos 

9757 

20° 

sin 

9 

.5341 

leg 

cos 

9 

.9730 

21° 

sin 

5543 

log 

cos 

9702 

22° 

sin 

5736 

log 

cos 

9672 

LOGARITHMS  OF  SINES  AND  COSINES 
10'        23'      30'      40'      5)'      6d'  A°  INTERPOLATION 

7.4637  7648  9408*0o58*1627*2419  cos  83°  Do  not  interpolate  between 
10.0000  0000  0000  0000  0000*9999  log   sin  log  sin  0°  and  log  sin  3°. 
3088  3668  4179  4637  5059  542S  cos  83°  In  the  interval  between 
9999  9999  9999  9998  9998  9997  leg   sin  log  sin  3°  and  log  sin  14°. 

interpolation  may  be  used 
5776  6097  6397  6677  6940  7188  cos  87°  with  the  actual  difference 
9997  9996  9996  9995  9995  9994  log  sin  obtained  by  subtraction 
7423  7645  7857  8059  8251  8436  cos  85°  with  a  possible  error 
9993  9993  9992  9991  9990  9989  log  sin  of  one  unit,  fourth  place. 
8613  8783  8946  9104  92-56  9403  cos  85°  Similarity  for  log  cos  87  °-90°, 
9989  9988  9987  9986  9985  9983  log  sin  do  not  interpolate: 

between  log  cos  76°  and  87° 
9545  9682  9816  9945*0070*0192  cos  84°  interpolation  may  be  used. 
9982  9981  9980  9979  9977  9976  log   sin 

0311  0426  0539  0648  0755  0859  cos  83°  Separate  tables  are  given 
9975  9973  9972  9971  9969  9968  log  sin  to  four  places,  giving 

log  sines  from  0°  to  14°  . 
0961    1060  1157  1252  1345  1436  cos  82°  by  minutes. 
9966  9964  9963  9961  9959  9958  log   sin 

1525  1612  1697   1781   1863   1943  cos  81  °  Mechanical  Interpolation 
9956  9954  9952  9950  9948  9946  log   sin  The  following  scheme  gives 
2022  2100  2176  2251  2324  2397  cos  80°  tenths  of  the  mean  difference 
9944  9942  9940  9938  9936  9934  log  sin  applying  throughout  the  line 

to  which  these  differences 
2468  2538  2606  2674  2740  2806  cos  79°  attach. 
9931  9929  9927  9924  9922  9919  log   sin  Regard  the  differences 
2870  2934  2997  3058  3119  3179  cos  78°  as  units  of  the  fourth  place; 
9917  9914  9912  9909  9907  9904  log   sin  they  change  the  last  place, 
10'      20'      30'      40'      50'      60'  A°      or  two  (sometimes  more) 

50'      40'      30'      20'      10'        0'  of  the  logarithm. 

3238  3296  3353  3410  3466  3521  cos  77°  An  error  of  one  unit 
9901  9899  9896  9893  9890  9887  log   sin  is  possible  in  the  last  place. 
3575  3629  3682  3734  3786  3837  cos  76° 

9884  9881  9878  9875  9872  9869  log   sin  12    3    4    5    6    7    8    9 

3887  3937  3986  4035  4083  4130  cos  75°  49    5  10  15  20  24  29  34  39  44 
9866  9863  9859  9856  9853  9849  log   sin  interpolate  mentally 

4177  4223  4269  4314  4359  4403  cos  74°  46    5    9  14  18  23  27  32  35  41 

9846  9843  9839  9836  9832  9828  log   sin      using  multiplication  table 

4447  4491  4533  4576  4618  4659  cos  73"  45    4    9  13  17  21  26  30  34  38 

9825  9821  9817  9814  9810  9806  log   sin         ,  for  small  differences 

4700  4741  4781  4821  4861  4900  cos  72°  40  4    8  12  16  20  24  28  32  36 

9802  9798  9794  9790  9786  9782  log   sin  mentally 

4939  4977  5015  5052  5090  5126  cos  71°  38  4    8  11  15  19  23  26  30  34 

9778  9774  9770  9765  9761  9757  log   sin  mentally 

5163  5199  5235  5270  5306  5341  cos  70°  36  4    7  11  14  IS  21  25  29  32 

9752  9748  9743  9739  9734  9730  log   sin 

5375  5409  5443  5477  5510  5543  cos  69°  34    3    7  10  13  17  20  24  27  30 
9725  9721  9716  9711  9706  9702  sin    log 

5576  5609  5641  5673  5704  5736  cos  68°  32    3    6  10  13  16  19  22  26  29 
9697  9692  9687  9682  9677  9672  log   sin 

5767  5798  5828  5859  5889  5919  cos  67°  30    3    6    9  12  15  18  21  24  27 
9667  9661  96-56  9651  9646  9640  log   sin 
50'      40'      30'      20'      10'        0'  A"  12    3    4    5    6    7    8    9 


—   14  — 


TABLE  IV 


LOGARITHMS  OF  SINES  AND  COSINES 
A"  0'       10'      20'      30'      40'      50'      60' 

23°  sin  9.5919  5948  5978  6007  6086  6065  6093  cos  66° 
loff  cos  9.9640  9635  9629  9624  9618  9613  9607  log  sin 
24°  sin  6093  6121  6149  6177  6205  6232  6259  cos  65° 
log  cos   9607  9602  9596  9590  9584  9579  9573  log  sin 

6259  6286  6313  6340  6366  6392  6418  cos  64° 
9573  9567  9561  9555  9549  9543  9537  log  sin 
6418  6444  6470  6495  6521  6546  6570  cos  63° 
9537  9530  9524  9518  9512  9505  9499  log  sin 
6570  6595  6620  6644  6668  6692  6716  cos  62° 
9499  9492  9486  9479  9473  9466  9459  log  sin 

6716  6740  6763  6787  6810  6833  6S56  cos  61° 
9459  9453  9446  9439  9432  9425  9418  log  sin 
sm   6856  6878  6901  6923  6946  6968  6990  cos  60° 
log  cos   9418  9411  9404  9397  9390  9383  9375  log  sin 

30°  sin  9.6990  7012  7033  7055  7076  7097  7118  cos  59° 

log  cos  9.9375  9368  9361  9353  9346  9338  9331  log  sin 

31°  sin  7118  7139  7160  7181  7201  7222  7242  cos  58° 

log  cos  9331  9323  9315  9308  9300  9292  9284  log  sin 

32°  sin  7242  7262  7282  7302  7322  7342  7361  cos  57° 

log  cos  9284  9276  9268  8260  9252  9244  9236  sin  log 


25° 

sin 

^ 

cos 

sin 

log 

cos 

27° 

sin 

log 

cos 

28° 

sin 

1.^1 

cos 

33° 

sin 

7361  7380  7400  7419  7438  7457  7476  cos  56" 

log 

cos 

9236  9228  9219  9211  9203  9194  9186  log  sin 

34° 

sin 

7476  7494  7513  7531  7550  7568  7586  cos  55° 

log 

cos 

9186  9177  9169  9160  9151  9142  9134  log  sin 

A 

0'   10'   20'   30'   40'   SO'   60'      A° 
60'  50'   40'  30'   20'   10'    0' 

35° 

sin 

7586  7604  7622  7640  7657  7675  7692  cos  54° 

log 

cos 

9134  9125  9116  9107  9098  9089  9080  log  sin 

36° 

sin 

7692  7710  7727  7744  7761  7778  7795  cos  53° 

log 

cos 

9080  9070  9061  9052  9042  9033  9023  log  sin 

37° 

sin 

7795  7811  782S  7844  7861  7877  7893  cos  52° 

log 

cos 

9023  9014  9004  8995  8985  8975  8965  log  sin 

38° 

sin 

7893  7910  7926  7941  7957  7973  7989  cos  51° 

log 

cos 

8965  8955  8945  8935  8925  8915  8905  log  sin 

39° 

sin 

7989  8004  8020  8035  8050  8066  8081  cos  50° 

log 

cos 

8905  8895  8884  8874  8864  8853  8843  log  sin 

40° 

sin 

9.8081  8096  8111  8125  8140  8155  8169  cos  49° 

log 

cos 

9.8843  8832  8821  8810  8800  8789  8778  log  sin 

41° 

sin 

8169  8184  8198  8213  8227  8241  8255  cos  48° 

i?° 

cos 

8778  8767  8756-8745  8733  8722  8711  log  sin 

sin 

8255  8269  8283  8297  8311  8324  8338  cos  47° 

log 

cos 

8711  8699  8688  8676  8665  8653  8641  log  sin 

43° 

sin 

8338  8351  8365  8378  8391  8405  8418  cos  46° 

^.■^ 

cos 

8641  8629  8618  8606  8594  8582  8569  log  sin 

sin 

8418  8431  8444  8457  8469  8482  8495  cos  45° 

%"' 

cos 

8569  8557  8545  8532  8520  8507  8495  log  sin 

sin 

8495  8507  8520  8532  8545  8557  8569  cos  44° 

log 

cos 

8495  8482  8469  8457  8444  8431  8418  log  sin 

Mean  DLferanc-ss 
d      12345      678    t» 

29    3    6    9  12  15  17  20  23  26 

interpolate  mentally 

28    3    6    8  11  14  17  19  22  25 

using  multiplication  table 

26  3  5  8  11  13  16  19  21  24 
for  small  differences 

25  3  5  8  10  13  15  18  20  23 
interpolate  mentally 

24  2  5  7  10  12  15  17  19  22 
for  small  differences 

23    2    5    7    9  12  14  16  19  21 

using  multiplication  table 
22    2    4    7    9  11  13  16  18  20 


21  2  4  6  9  11  13  15  17  19 
21  2  4  6  8  10  12  14  16  19 
20    2    4    6    8  10  12  14  16  18 

19  2  4  6  8  10  11  13  15  17 
18    2    4    6    7    9  11  13  15  17 

d      123456789 

18  2  4  5  7  9  11  12  14  16 
interpolate  mentally 

17  2  3  5  7  9  10  12  14  15 
using  multiplication  tables 

16  2  3  5  7  8  10  12  13  15 
for  small  differences 

16    2    3    5    6    8  10  11  13  14 

15    2    3    5    6    8    9  11  12  14 


15 

3 

4 

6 

7 

9  10  12  13 

11 

2 

3 

4 

5 

6  8  9  10 

14 

3 

4 

6 

7 

9  10  11  13 

11 

2 

3 

4 

6 

7  8  9  10 

14 

3 

4 

4 

7 

8  10  11  12 

12 

2 

3 

5 

6 

7  8  9  10 

13 

3 

4 

5 

7 

8  9  11  12 

12 

2 

4 

5 

6 

7  8  10  11 

13 

3 

4 

5 

6 

8  9  10  12 

12 

2 

4 

5 

6 

7  9  10  11 

12 

2 

4 

5 

6 

7  9  10  11 

13 

3 

4 

5 

6 

8  9  10  12 

d 

2 

3 

4 

5 

6  7  8  9 

TABLE  V 


LOGARITHMS  OF  TANGENTS  AND  COTANGENTS 

0'        10'        20'      30'      40'      50'      CO'  A°  INTERPOLATION 

4637  7648  9409*0658*1627*2419  cot    89 °  Do  not  interpolate  between 
5363  2352  0591*9342*8373*7581  log  tan  log  tan  0°  and  log  tan  3°. 
3089  3669  4181  4638  5053  5431  cot  8S°  or  log  cot  87°  andlog  cot  90°. 
6911  6331  5819  5362  4947  4569  log  tan 

In  the  interval  between 
5779  6101  6401  6682  6945  7194  cot  87°  log  tan  3°  and  log  tan  14°,  or 
4221  3899  3599  3318  3055  2806  log  tan  log  cot  76°  and  log  cot  87° 
7429  7652  7865  8067  8261  8446  cot  86°  interpolation  may  be  used 
2571   2348  2135  1933  1739  1554  log  tan  with  the  actual  difference 
8624  8795  8960  9118  9272  9420  cot  85°  obtained  by  subtraction 
1376  1205  1040  0882  0728  0580  log  tan  with  a  possible  error  of 

one  unit,  fourth  place. 
9563  9701  9836  9966*0093*0216  cot  84° 

0437  0299  0164  0034*9907*9784  lo?  tan  Separate  tables  are  given 
0336  0453  0567  0678  0786  0891  cot  83  °  with  four  place  values 
9664  9547  9433  9322  9214  9109  leg  tan  log  tan    0°  to  log  tan  14° 

log  cot  76°  to  log  cot  90° 
0995  1096  1194  1291   1385  1478  cot  82°  by  minutes. 
9005  8904  8806  8709  8615  8522  log  tan 

1569  1658  1745  1831   1915   1997  cot  81  °  Mechanical  Interpolation 
8431  8342  8255  8169  8085  8003  log  tan  The  following  scheme  gives 
2078  2158  2236  2313  2389  2463  cot  80°  tenths  of  the  mean  difference 
7922  7842  7764  7687  7611  7537  log  tan  applying  throughout  the  line 

to  which  attached. 
2536  2609  2680  2750  2819  2887  cot  79° 

7464  7391  7320  7250  7181  7113  log  tan  Regard  the  differences 
2953  3020  3085  3149  3212  3275  cot  78°  as  units  of  the  fourth  place; 
7047  6980  6915  6851  6788  6725  log  tan  they  change  the  last  place, 
10'      20'   30'      40'      50'       60'  A°   or  two  places  (or  more) 

50'      40'      30'      20'      10'        0'  of  the  logarithm. 

3336  3397  3458  3517  3576  3634  cot  77°  An  error  of  one  unit 
6664  6603  6542  6483  6424  6366  log  tan  is  possible  in  the  last  place. 
3691  3748  3804  3859  3914  3968  cot  76° 

6309  6252  6196  6141  6086  6032  log  tan  d  12  3  4  5  6  7  8  9 
4021  4074  4127  4178  4230  4281  cot  75°  52  5  10  16  21  26  31  36  42  47 
5979  5926  5873  5822  5770  5719  log  tan  52 

15°  tan  9.4281  4331  4381  4430  4479  4527  4575  cot74°    49    5  10  15  20  25  29  34  39  44 

log  cot  0.5719  5669  5619  5570  5521  5473  5425  log  tan  49 

16°  tan  9.4575  4622  4669  4716  4762  4808  4853  cot  73°  46    5    9  14  19  23  28  33  37  42 

log  cot  0.5425  5378  5331  5284  5238  5192  5147  log  tan  46 

17°  tan  9.4853  4898  4943  4987  5031   5075  5118  cot  72°  44    4    9  13  18  22  26  31  35  40 

log  cot  0.5147  5102  5057  5013  4969  4925  4882  log  tan  44 

18°  tan  9.5118  5161   5203  5245  5287  5329  5370  cot  71  °  42    4    8  13  17  21  25  29  34  38 

log  cot  0.4882  4839  4797  4755  4713  4671  4630  log  tan  42 

19°  tan  9.5370  5411   5451  5491   5531  5571  5611  cot  70°  40    4    8  12  16  20  24  28  32  36 

log  cot  0.4630  4589  4549  4509  4469  4429  4389  log  tan  40 

20°  tan  9.5611  5650  5689  5727  5766  5804  5842  cot  69°  39    4    8  12  15  19  23  27  31  35 

log  cot  0.4389  4350  4311  4273  4234  4196  4158  log  tan  ^9 

21  °  tan  9  .5842  5879  5917  5954  5991  6028  6064  cot  68°  37    4    7  11  15  19  22  26  30  33 

log  cot  0.4158  4121  4083  4046  4009  3972  3936  log  tan  37 

22°  tan  9.6064  6100  6136  6172  6208  6243  6279  cot  67°  36    4    7  11  14  18  21  25  29  32 

log  cot  0.3936  3900  3864  3828  3792  3757  3721  loe  tan  36 

A°  CO'  50'      40'      40'      20'      10'        0'        ~A°      d      1     2    3    4    5    6    7    8    9 


i6 


0° 

taT 

7 

log 

cot 

2 

1° 

tan  8 

.2419 

log   cot  1 

.7581 

2° 

tan  8 

.5431 

log 

cot  1 

.4569 

3° 

tan  8 

.7194 

^7^ 

cot  1 

.2806 

tan  8 

.8446 

log 

cot  1 

.1554 

5° 

tan  8.9420 

log 

cot  1 

.0580 

6° 

tan  9 

.0216 

log 

cot  0.9784 

7° 

tan  9 

.0891 

"? 

cotO 

.9109 

tan  9 

.1478 

log 

cotO 

.8522 

9° 

tan  9 

.1997 

log 

cot  0.8003 

10° 

tan  9 

.2463 

17 

cot  0 

.7537 

tan  9 

.2887 

^ 

cot  0 

.7113 

D 

0' 

60' 

12° 

tan  9 

.3275 

log  cot  0 .  6725 

13° 

tan  9 

.3634 

log 
14° 

cotO 

.6366 

tan  9 

.3968 

log 

cot  0 

.6032 

TABLE  V 


LOGARITHMS  OF  TANGENTS  AND  COTANGENTS  Mean  Differences 

A°  0'         10'      20'       30'      40'     50'     60'         A°  d      1     2    3    4    5    6    7    8    9 

23°  tan  9.6279  6314  6348  6383  6417  6452  6486  cot  66°  34    3    7  10  14  17  21  24  28  31 

log  cot  0.3721  3686  3652  3617  3583  3548  3514  log  tan  34 

24°  tan  9.6486  6520  6553  6587  6620  6654  6687  cot  65°  33    3    7  10  13  17  20  23  27  30 

log  cot  0.3514  3480  3447  3413  3380  3346  3313  log  tan  33 

25°  tan  9.6687  6720  6752  6785  6817  6850  6882  cot  64°  33    3    7  10  13  16  20  23  26  20 

log  cot  0.3313  3280  3248  3215  3183  3150  3118  log  tan  33 

26°  tan  9.6882  6914  6946  6977  7009  7040  7072  cot  63°  32    3    6    9  13  16  19  22  25  28 

log  cot  0.3118  3086  3054  3023  2991  2960  2928  log  tan  32 

27°  tan  9.7072  7103  7134  7165  7196  7226  7257  cot  62°  31     3    6    9  12  15  19  22  25  28 

log  cot  0.2928  2897  2866  2835  2804  2774  2743  log  tan  31 

28°  tan  9.7257  7287  7317  7348  7378  7408  7438  cot  61  °  30    3    6    9  12  15  18  21  24  27 

log  cot  0.2743  2713  2683  2652  2622  2592  2562  log  tan  30 

29°  tan  9.7438  7467  7497  7526  7556  7585  7614  cot  60°  29    3    6    9  12  15  18  21  24  27 

log  cot  0.2562  2533  2503  2474  2444  2415  2386  log  tan  29 

30°  tan  9.7614  7644  7673  7701  7730  7759  7788  cot  59°  29    3    6    9  12  14  17  20  23  26 

leg  cot  0.2386  2356  2327  2299  2270  2241  2212  log  tan  29 

31°  can  9.7788  7816  7845  7873  7902  7930  7958  cot  58°  28    3    6    9  11  14  17  20  23  26 

log  cot  0.2212  2184  2155  2127  2098  2070  2042  log  tan  28 

32°  tan  9.7958  7986  8014  8042  8070  8097  8125  cot  57°  28 

log  cot  0.2042  2014  1986  1958  1930  1903  1875  log  tan  28 

33°  tan  9.8125  8153  8180  8208  8235  8263  8290  cot  56°  27 

log  cot  0  1875  1847  1820  1792  1765  1737  1710  log  tan  27 

34°  tan  9.8290  8317  8344  8371  8398  8425  8452  cot  55°  27 

log  cot  0.1710  1683  1656  1629   1602  1575  1548  log  tan  27 
A°           0'        10'      20'   30'        40'      50'      60'           A° 

60'      50'      40'     30'       20'      10'       0'  A°  d 

35°  tan  9.8452  8479  8506  8533  8559  8586  8613  cot  54°  27 

leg  cot  0.1548  1521   1494  1467  1441   1414  1387  log  tan  27 

36°  tan  9.8613  8639  8666  8692  8718  8745  8771  cot  53°  26    3    5    8  11  13  16  18  21  24 

log  cot  0.1387   1361   1334  1308  1282  1255  1229  log  tan  26 

37°  tan  9.8771  8797  8824  8850  8876  8902  8928  cot  52°  26    3    5    8  10  13  16  18  21  24 

log  cot  0.1229   1203  1176  1150  1124  1098  1072  log  tan  26 

38°  tan  9.8928  8954  8980  9006  9032  9058  9084  cot  51°  26    3    5    8  10  13  16  18  21  23 

log  cot  0   1072  1046  1020  0994  0968  0942  0916  log  tan  26 

39°  tan  9.9084  9110  9135  9161  9187  9212  9238  cot  50°  26    3    5    8  10  13  15  18  21  23 

log  cot  0.0916  0890  0865  0839  0813  0788  0762  log  tan  26 

40°  tan  9.9238  9264  9289  9315  9341  0366  9392  cot  49°  26    3    5    8  10  13  15  18  21  23 

log  cot  0.0762  0736  0711  0685  0659  0634  0608  log  tan  26 

41°  tan  9.9392  9417  9443  9468  9494  9519  9544  cot  48°  25    3    5    8  10  13  15  18  20  23 

log  cot  0.0608  0583  0557  0532  0506  0481  0456  log  tan  25 

42°  tan  9.9544  9570  9595  9621  9646  9671  9697  cot  47°  25    3    5    8  10  13  15  18  20  23 

log  cot  0.0456  0430  0405  0379  0354  0329  0303  log  tan  25 

43°  tan  9.9697  9722  9747  9772  9798  9823  9848  cot  46°  25    3    5    8  10  13  15  18  20  23 

log  cot  0.0303  0278  0253  0228  0202  0177  0152  log  tan  25 

44°  tan  9.9848  9874  9899  9924  9949  9975*0000  cot  45°  25    3    5    8  10  13  15  18  20  23 

log   cot  0.0152  0126  0101  0076  0051  0025  0000  log  tan  25 

45°  tan  0  0000  0025  0051  0076  0101  0126  0152  cot  4-1°  25    3    5    8  10  13  15  18  20  23 

log   cot  0.0000*9975*9949*9924*9899*9874*9848  log  tan  25 

A°  CJ'      5J'      40'        30'   20'      10'        0'  A°  d      1    2    3    4    5    C    7    8    9 


7  — 


3  6 

8  11  14  17  19  22  25 

3  5 

8  11  14  16  19  22  25 

3  5 

8  11  14  16  19  22  24 

1  2 

3  5 

3  4  5  6  7  8  9 

8  11  13  16  19  21  24 

TABLE  VI 


L  Sin  L  Tan 

L  Sin  L  Tan  L  Sin  L  Tan 

L  Sin  L  Tan 

L  Sin  L  Tan 

LSin^ 

L  Tan  L  Sin  L  Tan 

0' 

0 

8.2419 

.2419 

.5428 

.5431 

.7188 

.7194 

.8436 

.8446  8.9403 

.9420  9.0192 

.0216 

60' 

1' 

6.4637 

.4637 

.2490 

.2491 

.5484 

5467 

.7212 

.7218 

.8454 

.  8465 

.9417 

.9434  9.0204 

.0228 

59' 

2' 

6 .  7648 

.7648 

.2561 

.2562 

.5500 

.5503 

.7236 

.7242 

.8472 

.8483 

.94.32 

.9419  9.0216 

.0240 

58' 

3' 

6.9408 

.9408 

.2630 

.2631 

.5535 

.5538 

.7260 

.7268 

.8490 

.8501 

.9448 

.9133  9.0228 

.0253 

57' 

4' 

7.0358 

.  0658 

.2699 

.2700 

.5571 

.5573 

.7283 

.7290 

.8508 

.8518 

.9460 

.9177  9.0240 

.0265 

56' 

5' 

7.1627 

.1627 

.2766 

.2767 

.5605 

.5308 

.7307 

.7313 

.8525 

.8536 

.9475 

.9192  9.0252 

.0277 

55' 

6' 

7.2419 

.2419 

.2832 

.2833 

.5640 

.5643 

.7330 

.7337 

.8543 

.8554 

.9189 

,9506  9.0234 

.0289 

54' 

7' 

7.3088 

.3088 

.2898 

.2899 

.5574 

.5677 

.7354 

.7360 

.8580 

.8572 

.9593 

.9520  9.0276 

.0300 

53' 

8' 

7.3668 

.3668 

.2982 

.2963 

.5708 

.5711 

.7377 

.  7383 

,8578 

.8589 

.9517 

.9534  9.0287 

.0312 

52' 

9' 

7.4180 

.4180 

.3025 

.3026 

.5742 

.5745 

.7400 

.7406 

.8595 

.8607 

.9531 

.9549  9.0299 

.0324 

51' 

10' 

7.4637 

.4637 

.3088 

.3089 

.5776 

.5779 

.7423 

.7429 

.8613 

.8624 

.9545 

.9563  9.0311 

.0336 

50' 

11' 

7.5051 

.5051 

.3150 

.3150 

.5809 

.5812 

.7445 

.7452 

.8630 

.  8042 

.9559 

.9577  9.0323 

.0343 

49 

12' 

7.5429 

.5429 

.3210 

.3211 

.5842 

.5845 

.7468 

.7475 

.8647 

.8659 

.9573 

.9591  9.0334 

.0360 

48' 

13' 

7.5777 

.5777 

.3270 

.3271 

.5875 

.5878 

.7491 

.7497 

.8665 

.8676 

.9587 

.9335  9.0346 

.0371 

47' 

14' 

7.6099 

.6099 

.3329 

.3330 

.5907 

.5911 

.7513 

.7520 

.8682 

.8694 

.9801 

.9319  9.0357 

.0383 

46' 

15' 

7.6398 

.6398 

.3388 

.3389 

.5939 

.5943 

.7535 

.7542 

.8899 

.8711 

.9814 

.9333  9.0370 

.0395 

45' 

16' 

7.6678 

.6678 

.3445 

.3446 

.5972 

.5975 

.7557 

.7565 

.8716 

.8728 

.9828 

.9316  9.0380 

.0107 

44' 

17' 

7.6942 

.6942 

.3502 

.3503 

.6003 

.6007 

.7580 

.7587 

.8733 

.8745 

.9842 

.9880  9.0392 

.0418 

43' 

18' 

7.7190 

.7190 

.3558 

..3559 

.6035 

.6038 

.7602 

.7609 

.8749 

.8762 

.9855 

.9874  9.0403 

.0430 

42' 

19' 

7.7425 

.7425 

.3613 

.3614 

.6066 

.6070 

.7623 

.7631 

.8766 

.8778 

.9669 

.9688  9.0415 

.0441 

41' 

20' 

7.7648 

.7648 

.3668 

.3669 

.6097 

.6101 

.7645 

.7652 

.8783 

.8795 

.9682 

.9701  9.0426 

.0453 

40' 

21' 

7.7859 

.7860 

.3722 

.3723 

.6128 

.6132 

.7667 

.7674 

.8799 

.8812 

.9896 

.9715  9.0438 

.0464 

39' 

22' 

7.8061 

.8062 

.3775 

.3776 

.6159 

.6163 

.7688 

.7696 

.8816 

.8829 

.9709 

.9729  9.0450 

.0476 

38' 

23' 

7.8255 

.8255 

.3828 

.3829 

.6189 

.6193 

.7710 

.7717 

.8833 

.8845 

.9723 

.9742  9.0460 

.0487 

37' 

24' 

7.8439 

.8439 

.3880 

.3881 

.6220 

.6223 

.7731 

.7739 

.8849 

.8862 

.9736 

.9756  9.0472 

.0499 

3C' 

25' 

7.8617 

.8617 

.3931 

.3932 

.6250 

.6254 

.7752 

.7760 

.8865 

.8878 

.9750 

.9769  9.0483 

.0510 

35' 

26' 

7.8787 

.8787 

.3982 

.3983 

.6279 

.6283 

.7773 

.7781 

.8882 

.8895 

.9763 

.9782  9.0494 

.0.521 

34' 

27' 

7.8951 

.8951 

.4032 

.4033 

.6309 

.6313 

.7794 

.7802 

.8898 

.8911 

.9776 

.9796  9.0505 

.0533 

33' 

28' 

7.9109 

.9109 

.4082 

.4083 

.6339 

.6.343 

.7815 

.7823 

.8914 

.8927 

.9789 

.9809  9.0516 

.0544 

32' 

29' 

7.9261 

.9261 

.4131 

.4132 

.6368 

.6372 

.7836 

.7844 

.8930 

.  8944 

.9803 

.9823  9.0527 

.0555 

31' 

L  Sin  L  Tan  L  Sin  L  Tan  L  Sin  L  Tan  L  Sin  L  Tan  L  Sin  L  Tan  L  Sin  L  Tan  L  Sin  L  Tan 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

30' 

7.9408 

9409 

.4179 

.4181 

.6397 

.6401 

.7857 

.7865 

.8946 

.8960 

.9816 

.98.36  9.0539 

.0567 

30' 

31' 

7-9551 

9551 

.4227 

.4229 

.6426 

.6430 

.7877 

.7886 

.8932 

.8976 

.9329 

.9349  9.0550 

.0578 

29' 

32' 

7.9.389 

9689 

.4275 

.4276 

.6454 

,6459 

.7898 

.7908 

.8978 

.8992 

.9312 

.9332  9.0561 

.0589 

2. 

33' 

7.9322 

9823 

.4322 

.4323 

.6483 

.6487 

.7918 

.7927 

.8994 

.9008 

.9355 

.9375  9.0572 

.0600 

27' 

34' 

7.9952 

.9952 

.4368 

.4370 

.6511 

.6515 

.7939 

.7947 

.9010 

.9024 

.9338 

.9338  9.0583 

.0611 

26' 

35' 

8.0078 

0078 

.4414 

.4416 

.6539 

.^544 

.7959 

.7967 

.9026 

.9040 

.9331 

.9931  9.0594 

.0622 

25' 

36' 

8.0200 

0200 

.4459 

.4461 

.6567 

.6571 

.7979 

.7988 

.9042 

.9056 

.9894 

.9915  9.0605 

.0633 

24' 

37' 

8.0319 

.0319 

.4504 

.4506 

.6595 

.6599 

.7999 

.8008 

.9057 

.9071 

.9907 

.9928  9.0616 

.0645 

23' 

38' 

8.0435 

.0435 

.4549 

.4551 

.6622 

.6627 

.8019 

.8028 

.9073 

.9087 

.9919 

.9940  9.0626 

.0656 

22' 

39' 

8.0548 

.0548 

,4593 

.4595 

.6650 

.6654 

.8039 

.8048 

.9089 

.9103 

.9932 

.9953  9.0637 

.0667 

21' 

40' 

8.0658 

.0658 

.4637 

.4638 

.6677 

.6682 

.8059 

.8067 

.9104 

.9118 

.9945 

.9966  9.0648 

.0678 

20' 

41' 

8.0765 

.0765 

.4680 

.4682 

.6704 

.6709 

.8078 

.8087 

.9119 

.9134 

.9958 

.9979  9.0659 

.0688 

19' 

42' 

8.0870 

.0870 

.4723 

.4725 

.6731 

.6736 

.8098 

.8107 

.9135 

.9150 

.9970 

.9992  9.0670 

.0699 

18' 

43' 

8.0972 

.0972 

.4765 

.4767 

.6758 

.6762 

.8117 

.8126 

.9150 

.9165 

.9983 

.0005  9.0680 

.0710 

17' 

44' 

8.1072 

.1072 

.4807 

.4809 

.6784 

.6789 

.8137 

.8140 

.9166 

.9180 

.9996 

.0017  9.0691 

.0721 

16' 

45' 

8.1169 

.1170 

.4848 

.4851 

.6810 

.6815 

.8156 

.8165 

.9181 

.9196  9 

.03:)8 

.0030  9.0702 

.0732 

15' 

46' 

8.1265 

.1265 

.4890 

.4892 

.6837 

.6842 

.8175 

.8185 

.9196 

.9211  9 

.0J21 

.0313  9.0712 

.0743 

14' 

47' 

8.1358 

.1359 

.49.30 

.4933 

.6883 

.6868 

.8194 

.8204 

.9211 

.9226  9 

.0333 

.0055  9.0723 

.0754 

13' 

48' 

8.1450 

.1450 

.4971 

.4973 

.6889 

.6894 

.8213 

.8223 

.9226 

.9211  9 

.0046 

.0038  r  0734 

.0764 

12' 

49' 

8.1539 

.1540 

.5011 

.5013 

.6914 

.6920 

.8232 

.8242 

.9241 

.9256  9.0058 

.0080  i  .0744 

.0775 

11' 

50' 

8.1627 

.1627 

.5050 

.5053 

.6940 

.6945 

.8251 

.8261 

.9256 

.9272  9 

.0070 

.0093  9.0755 

.0786 

10' 

51' 

8.1713 

.1713 

.5090 

.5092 

.6935 

.6971 

.8270 

.8280 

.9271 

.9237  9 

.0083 

.0105  9.0765 

.0796 

9' 

52' 

8.1797 

.1798 

.5129 

.5131 

.6991 

.6996 

.8289 

.8299 

.9286 

.9302  9 

.0095 

.0118  9.0776 

.0807 

8' 

53' 

8.1880 

.1880 

.5167 

.5170 

.7016 

.7021 

.8307 

.8317 

.9301 

.9316  9 

.0107 

.0130  9.0786 

.0818 

7' 

54' 

8.1961 

.1962 

.5206 

.5208 

.7041 

.7046 

.8326 

.8336 

.9315 

.9331  9 

.0120 

.0143  9.0797 

.0828 

6' 

55' 

8.2041 

.2041 

.5243 

.5246 

.7066 

.7071 

.8345 

.8355 

.9330 

.9346  9 

.0132 

.0155  9.0807 

.0839 

5' 

56' 

8.2119 

.2120 

.5281 

.5283 

.7090 

.7096 

.8363 

.8373 

.9345 

.9331  9 

.0144 

.0167  9.0818 

.0849 

4' 

57' 

8.2196 

.2196 

.5318 

.5321 

.7115 

.7121 

.8381 

.8392 

.9359 

.9376  9 

.0156 

.0180  9.0828 

.0860 

3' 

58' 

8.2271 

.2272 

.5355 

.5358 

.7140 

.7145 

.8400 

.8410 

.9374 

.9390  9 

.0168 

.0192  9.0838 

.0871 

2' 

59' 

8.2346 

.2346 

.5392 

.5394 

.7164 

.7170 

.8418 

.8428 

.9389 

.9405  9 

.0180 

.0204  9.0849 

.0881 

1' 

60' 

8.2419 
89° 

.2419 

.5428 
88° 

.5431 

.7188 
87° 

.7194 

.8436 
86° 

.8446 

.9403 
85° 

.9420  9 

.0192 
84' 

.0216  9.0859 
83° 

.0891 

0' 

L  Cos  L  Cot 

L  Cos  L  Cot 

L  Cos  L  Cot 

L  Cop 

L  Cot 

L  Cos 

L  Cot 

L  Co.- 

L  Cot  L  Cos 

L  Cot 

i8  — 


TABLE  VI. 


L  Sin 

L  Tan 

L  Sin  L  Tan 

„  Sin  L  Tan  L  Sin  L  Tan  L  Sin  L  Tan  L  Sin  L  Tan  L  Sin  L  Tan 

7° 

8 

° 

9 

° 

10° 

1] 

° 

12 

° 

13 

° 

0'   9 .  0859 

.0891 

.1436 

.1478 

.1943 

.1997 

.2397 

.2463 

.2806 

.2887 

.3179 

.3275 

.3521 

.3634  eC 

1'   9.0869 

.0902 

.1445 

.1487 

.1951 

.2005 

.2404 

.2471 

.2812 

.2893 

.3185 

.3281 

.3523 

.3639  59' 

2'   9.0879 

.0912 

.1453 

.1496 

.1959 

.2013 

.2411 

.2478 

.2819 

.2900 

.3191 

.3287 

.3532 

.3845  58' 

3'  9.0890 

.0923 

.1462 

A  COB 

.  1 967 

.2022 

.2418 

.2485 

.2825 

.2907 

.3197 

.3293 

.3337 

.3351  57' 

4'   9.0900 

.  0933 

.1471 

.1515 

.1975 

.2030 

.2425 

.2493 

,2832 

.2913 

.  3202 

..3300 

.3543 

.3657  56' 

5'   9.0910 

.0943 

.1480 

.1524 

.1083 

.2038 

.2432 

.2500 

.2838 

.2920 

.3208 

.3308 

.3548 

.3862  55' 

6'   9.0920 

.0954 

.1489 

.1533 

.1001 

.2046 

.2439 

.2507 

.2845 

.2927 

.3214 

.3312 

.3.554 

.3668  54' 

7'   9.0030 

.  0964 

.1498 

.1542 

.1099 

.  2054 

.2147 

.2515 

.2851 

.2934 

.3220 

.3?1S 

.3.559 

.3874  53' 

8'   9  0940 

.0974 

.1507 

.1551 

.2007 

.2062 

.2454 

.2522 

.2858 

.2940 

.3228 

.3324 

.3534 

.3680  52' 

9'   9.0951 

.0984 

.1516 

.1560 

.2015 

.2070 

.2461 

.2529 

.2864 

.2947 

.3232 

.3330 

.3570 

.3685  51' 

0'   9.0961 

.0995 

.  1525 

.1669 

.2022 

.2078 

.2468 

.2636 

.2870 

.2953 

.3238 

.3336 

.3576 

.3691  50' 

1'   9.0971 

.1005 

.1533 

.1578 

.2030 

.20S6 

.2475 

.2544 

.2877 

.2960 

.3244 

.3343 

.3581 

.3897  49' 

2'   9.09S1 

.1015 

.1542 

.  1587 

.203  5 

.2094 

.2482 

.2551 

.2883 

.2967 

.3253 

.3349 

.3586 

.3702  48' 

3'   9.0991 

.1025 

.1551 

.1596 

.2046 

.2102 

.24:9 

.2568 

.2890 

.2973 

.3255 

.  3355 

.3591 

.3708  47' 

4'   9.1001 

.1035 

.1560 

.1605 

.20.'')4 

.2110 

.2496 

.2565 

.2898 

.2980 

.3231 

.3361 

..3.597 

.3714  46' 

5'   9.1011 

.1045 

.1568 

.1613 

.2061 

.2118 

.2503 

.2573 

.2902 

.2987 

.3287 

.3367 

.3802 

.3719  45' 

6'   9.1020 

.  1 056 

.1577 

.1622 

.2069 

.2126 

.2510 

.2580 

.2909 

.2993 

.3273 

.3373 

.3338 

.3725  44' 

7'   9.1030 

.1066 

.1586 

.1631 

.2077 

.2134 

.2517 

.2587 

.2915 

.3000 

.3279 

.3379 

.3313 

.3731  43' 

8'   9.1040 

.1076 

.1594 

.1640 

.20.85 

.2142 

.2-)24 

.2594 

.2921 

..3006 

.32S4 

.  3385 

.3618 

.3736  42' 

9'   9.1050 

.1086 

.1603 

.1649 

.2092 

.2150 

.2531 

.2801 

.2928 

.3013 

.3290 

.3391 

.3624 

.3742  41' 

0'   9.1000 

.1096 

.1612 

.1058 

.2100 

.2158 

.2538 

.2809 

.2934 

.3020 

.3296 

.3397 

.3629 

.3748  40' 

1'   9.1070 

.1106 

.1620 

.  1667 

.2108 

.2166 

.2545 

.2616 

.2940 

.3026 

..3302 

.3403 

.3334 

.3753  39' 

;S'   9.10S0 

.1116 

.  1629 

.1675 

.2115 

.2174 

.2551 

.2323 

.2947 

.3033 

.3308 

.3409 

.3340 

.3759  38' 

3'   9.1089 

.1125 

.1637 

.1684 

.2123 

.2181 

.2558 

.2630 

.2953 

.  3039 

.3313 

.3416 

.3645 

.3764  37' 

4'   9.1099 

.1135 

.1646 

.1693 

.2131 

.2189 

.2585 

.2637 

.2959 

.3046 

.3319 

.3422 

.3650 

.3770  36' 

5'   9.1109 

.1145 

.  1655 

.1702 

.2138 

.2197 

.2572 

.2644 

.2935 

.3052 

.3325 

.3428 

.3655 

.3776  35' 

6'   9. Ills 

.1155 

.  1663 

.1710 

.2148 

.2205 

.2579 

.2651 

.2972 

.3059 

.3331 

.3434 

.3361 

.3781  34' 

7'   9.1128 

.1165 

.  1672 

.1719 

.2153 

.2213 

.2586 

.2658 

.2978 

.3065 

.3336 

.3440 

.3866 

.3787  33' 

8'   9.1138 

.1175 

.1680 

.1728 

.2181 

.2221 

.2.593 

.2666 

.2984 

.3072 

.3342 

.3446 

.3871 

.3792  32' 

9'   9.1147 

.1185 

.1689 

.1736 

.2169 

.2228 

.2800 

.2673 

.2990 

.3078 

.3348 

.3452 

.3677 

.3798  31' 

7° 

8° 

9" 

10° 

11° 

12° 

13" 

0'   9.1157 

.1194 

.1697 

.1745 

.2176 

.2236 

.2606 

.2680 

.2997 

.3085 

.3353 

.3458 

.3882 

.3804  30' 

1'   9.1167 

.1204 

.1705 

.1754 

.2184 

.2244 

.2613 

.2687 

.3003 

.3091 

.3359 

.3464 

.3687 

.3809  29' 

2'   9.1176 

.1214 

.1714 

.1762 

.2191 

.2252 

.  2320 

.  2694 

.3009 

.3098 

.3365 

.  3469 

.3092 

.3815  28' 

3'   9.1186 

.1223 

.1722 

.1771 

.2199 

.2259 

.2327 

.2701 

.3015 

.3104 

.3370 

.3475 

.3698 

.3820  27' 

4'   9.1195 

.1233 

.1731 

.1779 

.2206 

.2267 

.2634 

.2708 

.3021 

.3110 

.3376 

.3481 

.3703 

.3826  26' 

5'   9.1205 

.1243 

.1739 

.1788 

.2214 

.2275 

.2640 

.2715 

.3027 

.3117 

.3382 

.3487 

.3708 

.3831  25' 

6'   9.1214 

.1252 

.1747 

.1797 

.2221 

.2282 

.2647 

.2722 

.3034 

.3123 

.3387 

.3493 

.3713 

.3837  24' 

T      9.1224 

.1262 

.1756 

.1805 

.2229 

.2290 

.2654 

.2729 

.3040 

.3130 

.3393 

.  3499 

.3719 

.3842  23' 

8'   9.1233 

.1272 

.1764 

.1814 

.2236 

.2298 

.2661 

.2736 

.3046 

.3136 

.3399 

.3505 

.3724 

.3848  22' 

9'   9.1242 

.1281 

.1772 

.1822 

.2243 

.2305 

.2667 

.2743 

.3052 

.3142 

.3404 

.3511 

.3729 

.3853  21' 

0'   9.1252 

.1291 

.1781 

.1831 

.2251 

.2313 

.2674 

2750 

.3058 

3149 

.3410 

.3517 

.3734 

.3859  20' 

1'   9.1261 

.1300 

.1789 

.1839 

.2258 

.2321 

.2681 

2757 

.3064 

3155 

.3416 

.3523 

.3739 

.3864  19' 

2'   9.1271 

.1310 

.1797 

1848 

.2286 

.2328 

.2887 

2764 

.3070 

3162 

.3421 

.3529 

.3745 

.3870  18' 

3'   9.1280 

.1319 

.1806 

.1856 

.2273 

.2336 

.2894 

.2770 

.3077 

.3168 

.3427 

.3535 

.3750 

.3875  17' 

4'   9.1289 

.1329 

.1814 

.1864 

.2280 

.2343 

.2701 

.2777 

.3083 

3174 

.3432 

.3541 

..3755 

.3881  16' 

5'   9.1299 

.1338 

.1822 

.1873 

.2288 

2351 

.2707 

2784 

.3089 

3181 

.3438 

.3546 

.3760 

.3886  15' 

6'   9.1308 

.1348 

.1830 

.1881 

.2295 

.2359 

.2714 

2791 

.3095 

3187 

.3444 

.3552 

.3765 

.3892  14' 

7'   9.1317 

.1357 

.1838 

.1890 

.2333 

.2366 

.2721 

.2798 

.3101 

.3193 

.3449 

.3558 

.3770 

.3897  13' 

8'   9.1326 

.1367 

.1847 

.1898 

.2310 

.2374 

.2727 

.2805 

.3107 

.3200 

.3455 

.3564 

.3775 

.3903  12' 

9'   9.1336 

.1376 

.1855 

.1906 

.2317 

.2381 

.2734 

.2812 

.3113 

.3206 

.3460 

.3670 

.3781 

.3908  11' 

0'   9.1345 

.1385 

.1863 

1915 

.2324 

.2389 

.2740 

2819 

.3119 

3212 

.3466 

3576 

.3786 

.3914  10' 

r   9.1354 

.1395 

.1871 

1923 

.2332 

.2396 

.2747 

2825 

.3125 

3219 

.3471 

3581 

.3791 

.3919  9' 

2'   9.1363 

.1404 

.  1379 

.1931 

.2339 

.2404 

.2751 

2832 

.3131 

3225 

.3477 

3587 

.3796 

.3924  8' 

3'   9.1372 

.1413 

.1887 

1940 

.2346 

.2411 

.2730 

2839 

.3137 

3231 

.3482 

.3593 

.3801 

.  3930  7' 

4'   9.1381 

.1423 

.1895 

.1948 

.2353 

.2419 

.2767 

2846 

.3143 

3237 

.3488 

.3599 

.3806 

.3935  6' 

5'   9.1390 

.1432 

.1933 

.1956 

.2361 

.2426 

.2773 

2853 

.3149 

3244 

.3493 

.3605 

.3811 

.3941  5' 

6'   9.1399 

.1441 

.1911 

.1984 

.2338 

.2434 

.2780 

2859 

.3155 

3250 

.3499 

3611 

..3816 

.3946  4' 

7'   9.1409 

.1450 

.1919 

.1973 

.2375 

.2441 

.2786 

2866 

.3161 

3256 

.3504 

3616 

.3822 

3952  3' 

8'   9.1418 

.1460 

.1927 

1981 

.2382 

.2448 

.2793 

.2873 

.3167 

3262 

.3510 

3622 

.3827 

3957  2' 

0'      9.1427 

.1469 

.1935 

1989 

.2390 

.2456 

.2799 

2880 

.3173 

.3269 

.3515 

3628 

.3832 

.3962  1' 

0'   9.1436 

.1478 

.1943 

.1997 

.2397 

2463 

.2806 

.2887 

.3179 

.3275 

.3521 

.3634 

.3837 

.3968  tf 

82" 

81" 

80" 

79" 

78" 

77° 

76° 

L  Co.  L  Cot  L  Co.  L  Cot  L  Co.  L  Cot  L  Co.  L  Cot  L  Co.  L  Cot  L  Co.  L  Cot  L  Co.  L  Cot 

19  — 


TABLE  VII 


NUMERICAL  VALUES  OF  SINES 


A° 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

A° 

d. 

P.  P 

0 

0.0000 

0029 

0058 

0087 

0116 

0145 

0175 

89 

29 

30 

29 

1 

0175 

0204 

0233 

0262 

0291 

0320 

0349 

88 

29 

1 

3.0 

2.9 

2 

0349 

0378 

0407 

0436 

0465 

0494 

0523 

87 

29 

2 

6.0 

5.8 

3 

0523 

0552 

0581 

0610 

0640 

0669 

0698 

86 

29 

3 

9.0 

8.7 

4 

0698 

0727 

0756 

0785 

0814 

0843 

0872 

85 

29 

4 
5 

12.0 
15.0 

11.6 
14.5 

5 

0.0872 

0901 

0929 

0958 

0987 

1016 

1045 

84 

29 

6 

18.0 

17.4 

6 

1045 

1074 

1103 

1132 

1161 

1190 

1219 

83 

29 

7 

21.0 

20.3 

7 

1219 

1248 

1276 

1305 

1334 

1363 

1392 

82 

29 

8 

24.0 

23.2 

8 

1392 

1421 

1449 

1478 

1507 

1536 

1564 

81 

29 

9 

27.0 

26.1 

9 

1564 

1593 

1622 

1650 

1679 

1708 

1736 

80 

29 

28 

2.8 

27 

2.7 

10 

0.1736 

1765 

1794 

1822 

1851 

1880 

1908 

79 

29 

1 

11 

1908 

1937 

1965 

1994 

2022 

2051 

2079 

78 

28 

2 

5.6 

5.4 

12 

2079 

2108 

2136 

2164 

2193 

2221 

2250 

77 

28 

3 

8.4 

8.1 

13 

2250 

2278 

2306 

2334 

2363 

2391 

2419 

76 

28 

4 

11.2 

10.8 

14 

2419 

2447 

2476 

2504 

2532 

2560 

2588 

75 

28 

5 
6 

14.0 
16.8 

13.5 
16.2 

15 

0.2588 

2616 

2644 

2672 

2700 

2728 

2756 

74 

28 

7 

19.6 

18.9 

16 

2756 

2784 

2812 

2840 

2868 

2896 

2924 

73 

28 

8 

22.4 

21.6 

17 

2924 

2952 

2979 

3007 

3035 

3062 

3090 

72 

28 

9 

25.2 

24.3 

18 

3090 

3118 

3145 

3173 

3201 

3228 

3256 

71 

28 

19 

3256 

3283 

3311 

3338 

3365 

3393 

3420 

70 

27 

26 

25 

A« 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

d. 

1 

2.6 

2.5 

20 

0.3420 

3448 

3475 

3502 

3529 

3557 

3584 

69 

27 

2 

5.2 

5.0 

21 

3584 

3611 

3638 

3665 

3692 

3719 

3746 

68 

27 

3 

7.8 

7.5 

22 

3746 

3773 

3800 

3827 

3854 

3881 

3907 

67 

27 

4 

10.4 

10.0 

23 

3907 

3934 

3961 

3987 

4014 

4041 

4067 

66 

27 

5 

13.0 

12.5 

24 

4067 

4094 

4120 

4147 

4173 

4200 

4226 

65 

26 

6 

7 

15.6 
18.2 

15.0 
17.5 

25 

0.4226 

4253 

4279 

4305 

4331 

4358 

4384 

64 

26 

8 

20.8 

20.0 

26 

4384 

4410 

4436 

4462 

4488 

4514 

4540 

63 

26 

9 

23.4 

22.5 

27 

4540 

4566 

4592 

4617 

4643 

4669 

4695 

62 

26 

28 

4695 

4720 

4746 

4772 

4797 

4823 

4848 

61 

26 

24 

23 

29 

4848 

4874 

4899 

4924 

4950 

4975 

5000 

60 

25 

1 

2 

2.4 
4.8 

2.3 
4.6 

30 

0.5000 

5025 

5050 

5075 

5100 

5125 

5150 

59 

25 

3 

7.2 

6.9 

31 

5150 

5175 

5200 

5225 

5250 

5275 

5299 

58 

25 

4 

9.6 

9.2 

32 

5299 

5324 

5348 

5373 

5398 

5422 

5446 

57 

24 

5 

12.0 

11.5 

33 

5446 

5471 

5495 

5519 

5544 

5568 

5592 

56 

24 

6 

14.4 

13.8 

34 

5592 

5616 

5640 

5664 

5688 

5712 

5736 

.55 

24 

7 
8 

16.8 
19.2 

16.1 
18.4 

35 

0.5736 

5760 

5783 

5807 

5831 

5854 

5878 

54 

24 

9 

21.6 

20.7 

36 

5878 

5901 

5925 

5948 

5972 

5995 

6018 

53 

23 

37 

6018 

6041 

6065 

6088 

6111 

6134 

6157 

52 

23 

22 

21 

20 

38 

6157 

6180 

6202 

6225 

6248 

6271 

6293 

51 

23  1 

2. 

2   2.1 

2.0 

39 

6293 

6316 

6338 

6361 

6383 

6406 

6428 

50 

22  2 
3 

4. 
6. 

4   4.2 
6   6.3 

4.0 
6.0' 

40 

0.6428 

6450 

6472 

6494 

6517 

6539 

6561 

49 

22.  4 

8. 

8   8.4 

8.0 

41 

6561 

6583 

6604 

6626 

6648 

6670 

6691 

48 

22  5 

11. 

0  10.5 

10.0 

42 

6691 

6713 

6734 

6756 

6777 

6799 

6820 

47 

22  6 

13. 

2  12.6 

12.0 

43 

6820 

6841 

6862 

6884 

6905 

6926 

6947 

46 

21  7 

15. 

4  14.7 

14.0 

44 

6947 

6967 

6988 

7009 

7030 

7050 

7071 

45 

21  8 

17.6  16.8 

16.0 

A° 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

A° 

d.  9 

19. 

8  18.9 

18.0 

NUMERICAL  VALUES  OF  COSINES 

P.  P. 

TABLE  VII 


NUMERICAL  VALUES  OF  SINES 


A" 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

A" 

d. 

Proporti 

ional  Parts 

45 

0.7071 

7092 

7112 

7133 

7153 

7173 

7193 

44 

20 

21 

20 

19 

4'5 

7193 

7214 

7234 

7254 

7274 

7294 

7314 

43 

20 

1 

2.1 

2.0 

1.9 

47 

7314 

7333 

7353 

7373 

7392 

7412 

7431 

42 

20 

2 

4.2 

4.0 

3.8 

4S 

7431 

7451 

7470 

7490 

7509 

7528 

7547 

41 

19 

3 

6.3 

6.0 

5.7 

49 

7547 

7566 

7585 

7604 

7623 

7642 

7660 

40 

19 

4 
5 

8.4 
10.5 

8.0 
10.0 

7.6 
9.5 

51 

0.7660 

7679 

7698 

7716 

7735 

7753 

7771 

39 

18 

6 

12.6 

12.0 

11. -4 

51 

7771 

7790 

7808 

7826 

7844 

7862 

7880 

38 

18 

7 

14.7 

14.0 

13.3 

5? 

7880 

7898 

7916 

7934 

7951 

7969 

7986 

37 

18 

8 

16.8 

16.0 

15.2 

51 

7986 

8004 

8021 

8039 

8056 

8073 

8090 

36 

17 

9 

18.9 

18.0 

17.1 

54 

8090 

8107 

8124 

8141 

8158 

8175 

8192 

35 

17 

S5 

0.8192 

8208 

8225 

8241 

8258 

8274 

8290 

34 

16 

18 

17 

16 

56 

8290 

8307 

8323 

8339 

8355 

8371 

8387 

33 

16 

1 

1.8 

1.7 

1.6 

57 

8387 

8403 

8418 

8434 

8450 

8465 

8480 

32 

16 

2 

3.6 

3.4 

3.2 

58 

8480 

8496 

8511 

8526 

8.542 

8557 

8572 

31 

15 

3 

5.4 

5.1 

4.8 

59 

8572 

8587 

8601 

8616 

8631 

8646 

8660 

30 

15 

4 
5 

7.2 
9.0 

6.8 
8.5 

6.4 
8.0 

60 

0.8660 

8675 

8689 

8704 

8778 

8732 

8746 

29 

14 

6 

10.8 

10.2 

9.6 

61 

8746 

8760 

8774 

8788 

8802 

8816 

8829 

28 

It 

7 

12.6 

11.9 

11.2 

62 

8829 

8843 

8857 

8870 

8884 

8897 

8910 

27 

14 

8 

14.4 

13.6 

12.8 

63 

8910 

8923 

8936 

8949 

8962 

8975 

8988 

25 

13 

9 

16.2 

15.3 

14.4 

64 

8988 

9001 

9013 

9026 

9038 

9051 

9063 

25 

12 

A" 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

A° 

d. 

65 

0.9063 

9075 

9088 

9100 

9112 

9124 

9135 

24 

12 

15 

14 

13 

66 

9135 

9147 

9159 

9171 

9182 

9194 

9205 

23 

12 

1 

1.5 

1.4 

1.8 

67 

9205 

9216 

9228 

9239 

9250 

9261 

9272 

22 

11 

2 

3.0 

2.8 

2.6 

68 

9272 

9283 

9293 

9304 

9315 

9325 

9336 

21 

11 

3 

4.5 

4.2 

3.9 

69 

9336 

9346 

9356 

9367 

9377 

9387 

9397 

20 

10 

4 
5 

6.0 
7.5 

5.6 
7.0 

5.2 
6.5 

70 

0.9397 

9407 

9417 

9426 

9436 

9446 

9455 

19 

10 

0 

9.0 

8.4 

7.8 

71 

9455 

9405 

9474 

9483 

9492 

9502 

9511 

18 

9 

7 

10.5 

9.8 

9.1 

72 

9511 

9520 

9528 

9537 

9546 

9555 

9563 

17 

9 

8 

12.0 

11.2 

10.4 

73 

9.563 

9572 

9580 

9588 

9596 

9605 

9613 

16 

8 

9 

13.5 

12.6 

11.7 

74 

9613 

9621 

9628 

9636 

9644 

9652 

9659 

15 

8 

75- 

0.9659 

9667 

9674 

9681 

8689 

9696 

9703 

14 

7 

12 

11 

76 

9703 

9710 

9717 

9724 

9730 

9737 

9744 

13 

7 

1 

1.2 

1.1 

77 

9744 

9750 

9757 

9763 

9769 

9775 

9781 

12 

6 

2 

2.4 

2.2 

78 

9781 

9787 

9793 

9799 

9805 

9811 

9816 

11 

6 

3 

3.6 

3.3 

79 

9816 

9822 

9827 

9833 

9833 

9843 

9848 

10 

5 

4 
5 

4.8 
6.0 

4.4 
5.5 

80 

0.9848 

9853 

9858 

9863 

9868 

9872 

9877 

9 

5 

6 

7.2 

6.6 

81 

9877 

9S81 

9886 

9890 

9894 

9899 

9903 

8 

4 

7 

8.4 

7.7 

82 

9903 

9907 

9911 

9914 

9918 

9922 

9925 

7 

4 

8 

9.6 

8.8 

83 

9925 

9029 

9932 

9936 

9939 

9942 

9945 

6 

3 

9 

10.8 

9.9 

84 

9945 

9948 

9951 

9954 

9957 

9959 

9962 

5 

3 

F5 

0.9962 

9964 

9967 

9969 

9971 

9974 

9976 

4 

2 

For  differences  be- 

86 

9976 

9978 

9980 

9981 

9983 

9985 

9986 

3 

2 

Inw   10 

interpolate 

87 

9986 

9988 

9989 

9990 

9992 

9993 

9994 

2 

1 

mentally. 

empl< 

ayinjr 

88 

9994 

9995 

9996 

9997 

9997 

9998 

9998 

1 

1 

the  ordinary  multipli- 

89 

9998 

9999 

9999 

*0900 

*0000  *0000  *0000 

0 

0 

cation  table. 

A' 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

A° 

d. 

NUMERICAL  VALUES  OF  COSINES 


TABLE  VIII 


NUMERICAL  VALUES  OF  THE  TANGENT  FUNCTION 


A" 

0' 

10' 

20' 

30' 

40' 

50' 

60'  A°d.           P.P. 

0  0.0000 

0029 

0058 

0087 

0116 

0145 

0175  89  29    29   30   31   32   33 

1 

0175 

0204 

0233 

0262 

0291 

0320 

0349  88  29  1  2.9  3.0  3.1  3.2  3.3 

2 

0349 

0378 

0407 

0437 

0465 

0495 

0524  87  29  2  5.8  6.0  6.2  6.4  6.6 

3 

0524 

0553 

0582 

0612 

0641 

0670 

06998629  3  8.7  9.0  9.3  9.6  9.9 

4 

0699 

0729 

0758 

0787 

0816 

0846 

0875  85  29  4  11.6  12.0  12.4  12.8  13.2 
5  14.5  15.0  15.5  16.0  16.5 

5  0.0875 

0904 

0934 

0963 

0992 

1022 

105184  29  6  17.4  IS.O  18.6  19.2  19.8 

6 

1051 

1080 

1110 

11-39 

1169 

1198 

1228  83  30  7  20.3  21.0  21.7  22.4  23.1 

7 

1228 

1257 

1287 

1317 

1346 

1376 

1405  82  30  8  23.2  24.0  24.8  25.6  26.4 

8 

1405 

1435 

1465 

1495 

1564 

1554 

1.584  81  30  9  26.1  27.0  27.9  28.8  29.7 

9 

1584 

1614 

1644 

1673 

1703 

1733 

1763  80  30 

34   35   36   37   38 

10  0.1763 

1793 

1823 

1853 

1883 

1914 

1944  7930  1  3.4  3.5  3.6  3.7  3.8 

11 

1944 

1974 

2004 

2035 

2065 

2095 

21267830  2  6.8  7.0  7.2  7.4  7.6 

12 

2126 

2156 

2186 

2217 

2247 

2278 

2309  77  30  3  10.2  10.5  10.8  11.1  11.4 

13 

2.309 

2339 

2370 

2401 

2432 

2462 

2493  7631  4  13.6  14.0  14.4  14.8  15.2 

14 

2493 

2524 

2555 

2586 

2617 

2648 

2679  75  31  5  17.0  17.5  18.0  18.5  19.0 
6  20.4  21.021.6  22.2  22.8 

15  0.2679 

2711 

2742 

2773 

2805 

2836 

2867  74  31  7  23.824.525.225.926.6 

16 

2867 

2899 

2931 

2962 

2994 

3026 

3057  73  32  8  27.2  28.0  28.8  29.6  30.4 

17 

3057 

3089 

3121 

3153 

3185 

3217 

3249  72  32  9  30.6  31.5  32.4  33.3  34.2 

18 

3249 

3281 

3314 

3346 

3378 

3411 

3443  71  32 

19 

3443 

3476 

3508 

3541 

3574 

3607 

3640  70  33    39   40   41   42   43 

1  3.9  4.0  4.1  4.2  4.3 

A° 

0' 

10' 

20' 

30' 

40' 

50' 

60'  A°d.  2  7.8  8.0  8.2  8.4  8.6 
3  11.7  12.0  12.3  12.6  12.9 

20  0 

1.3640 

3673 

3706 

3/39 

3772 

3805 

38.39  69  33  4  15.6  16.0  16.4  16.8  17.2 

21 

3839 

3872 

3906 

3939 

3973 

4006 

4040  68  34  5  19.5  20.0  20.5  21.0  21.5 

22 

4040 

4074 

4108 

4142 

4176 

4210 

4245  67  34  6  23.4  24.0  24.6  25.2  25.8 

23 

4245 

4279 

4314 

4348 

4383 

4417 

4452  66  34  7  27.3  28.0  28.7  29.4  30.1 

24 

4452 

4487 

4522 

4557 

4592 

4628 

4663  65  35  8  31.2  32.0  32.8  33.6  34.4 
9  35.1  36.0  36.9  37.8  38.7 

25  0.4663 

4699 

4734 

4770 

4806 

4841 

4877  64  36 

26 

4877 

4913 

4950 

4986 

5022 

5059 

5095  63  36    44   45   46   47   48 

27 

5095 

5132 

5169 

5206 

5243 

5280 

53176237  1  4.4  4.5  4.6  4.7  4.8 

28 

5317 

5354 

5392 

5430 

5467 

5505 

5543  6138  2  8.8  9.0  9.2  9.4  9.6 

29 

5543 

5581 

5619 

5658 

5696 

5735 

577460  38  3  13.2  13.5  13.8  14.1  14.4 
4  17.6  18.0  18.4  18.8  19.2 

30  0.5774 

5812 

5851 

5890 

5930 

5969 

6009  59  39  5  22.0  22.5  23.0  23.5  24.0 

31 

6009 

6048 

6088 

6128 

6168 

6208 

6249  58  40  6  26.4  27.0  27.6  28.2  28.8 

32 

6249 

6289 

6330 

6371 

6412 

6453 

6494  5741  7  30.831.532.232.933.6 

33 

6494 

6536 

6577 

6619 

6661 

6703 

6745  56  42  8  35.2  36.0  36.8  37.6  38.4 

34 

6745 

6787 

6830 

6873 

6916 

6959 

7002  55  43  9  39.6  40.5  41.4  42.3  43.2 

35  0 

.7002 

7046 

7089 

7133 

7177 

7221 

7265  54  44   50   52   54   56   58 

36 

7265 

7310 

7355 

7400 

7445 

7490 

75365345  1  5.0  5.2  5.4  5.6  5.8 

37 

7536 

7581 

7627 

7673 

7720 

7766 

781352  46  2  10.0  10.4  10.8  11.2  11.6 

38 

7813 

7860 

7907 

7954 

8002 

8050 

8098  51  48  3  15.0  15.6  16.2  16.8  17.4 

39 

8098 

8146 

8195 

8243 

8292 

8342 

839150  49  4  20.0  20.8  21.6  22.4  23.2 
5  25.0  26.0  27.0  28.0  29. 

40  0.8391 

8441 

8491 

8541 

8591 

8642 

8693  49  50  6  30.0  31.2  32.4  33.6  34.8 

41 

8693 

8744 

8796 

8847 

8899 

8952 

9004  48  52  7  35.0  36.4  37.8  39.2  40.6 

42 

9004 

9057 

9110 

9163 

9217 

9271 

932547  54  8  40.0  41.6  43.2  46.8  46.4 

43 

9325 

9380 

9435 

9490 

9545 

9601 

96.57  46  55  9  45.0  46.8  48.6  50.4  52.2 

44 

9657 

9713 

9770 

9827 

9884 

9942 

0000  45  57 

60' 

50' 

40' 

30' 

20' 

10' 

0'  A°d.           P.P. 

NUMERICAL  VALUES  OF  COTANGENTS 

TABLE  VIII 


NUMERICAL  VALUES  OF  THE  TANGENT  FUNCTION 
A°        0'  10'        20'  30'  40'         50'  60'     A°  d.  P.  P. 

45  1.000     1.006     1.012       1.018       1.024     1.030     1.036  44     6        12       13       14       15 

46  1.036     1.042     1.048       1.054       1.060     1.066     1.072  43     6  1     1.2     1.3     1.4     1.5 

47  1.072     1.079     1.085       1.091        1.098     1.104     1.111  42     6  2    2.4     2.6     2.8     3.0 

48  1.111      1.117     1.124        1.130       1.137     1.144     1.150  41     6  3    3.6     3.9     4.2     4.5 

49  1.150     1.157     1.164       1.171        1.178     1.185     1.192  40     7  4    4.8     5.2     5.6     6.0 

5  6.0     6.5     7.0     7.5 

50  1.192  1.199  1.206   1.213   1.220  1.228  1.235  39  7  6  7.2  7.8  8.4  9.0 

51  1.235  1.242  1.250   1.257   1.265  1.272  1.280-38  8  7  8.4  9.1  9.8  10.5 

52  1.280  1.288  1.295   1.303   1.311  1.319  1.327  37  8  8  9.6  10.4  11.2  12.0 

53  1.327  1.335  1.343   1.351   1.360  1.368  1.376  36  8  9  10.8  11.7  12.6  13.5 

54  1.376  1.385  1.393   1.402   1.411  1.419  1.428  35  9 

17   18   19   20 

55  1.428     1.437     1.446       1.455       1.464     1.473     1.483  34     9  1    1.7     1.8     1.9     2.0 

56  1.483     1.492     1.501        1.511        1.520     1.530     1.540  33  10  2    3.4     3.6     3.8     4.0 

57  1.540     1.5.50     1.560       1.570       1.580     1.590     1.600  32  10  3    5.1     5.4     5.7     6.0 

58  1.600     1.611     1.621       1.632       1.643     1.653     1.664  31  11  4    6.8     7.2     7.6     8.0 

59  1.664     1.675     1.686       1.698       1.709     1.720     1.732  30  11  5    8.5    9.0     9.5  10.0 

6  10.2  10.8  11.4  12.0 

60  1.732     1.744     1.75-)       1.767       1.780     1.792     1.8042912711.912.613.311.0 

61  1.804     1.816     1.829       1.842       1.855     1.868     1.88128  13  8  13.6  14.4  15.2  18.0 

62  1.881     1.894     1.907       1.921       1.935     1.949     1.963  27  14  9  15.3  16.2  17.118.0 

63  1.963     1.977     1.991       2.006       2.020     2.035     2.050  26  14 

64  2.050     2.066     2.081       2.097       2.112     2.128     2.145  25  16        22       23       24       25 

1      9P'9^      94.      2*^ 
A°      0'  10'  20'  30'  40'  50'  60'    A°    d.   2    4.4     4^6     4^8     5  0 

3  6.6     6.9     7.2     7.5 

65  2.145  2.161  2.177   2.194   2.211  2.229  2.246  24  17  4  8.8  9.2  9.6  10.0 

66  2.246     2.264     2.282       2.300       2.318     2.337     2.3562318511.011.512.012.5 

67  2.356     2.375     2.394       2.414       2.434     2.455     2.475  22  20  6  13.2  13.8  14.4  15.0 

68  2.475     2.496     2.517       2.539       2.560     2.583     2.605  2122  7  15.4  16.116.8  17.5 

69  2.605     2.628     2.651       2.675       2.699     2.723     2.747  20  24  8  17.6  18.4  19.2  20.0 

9  19.8  20.7  21.6  22.5 

70  2.747     2.773     2.798       2.824       2.850     2.877     2.904  19  26 

71  2.901     2.932     2.960       2.989       3.018     3.047     3.078  18  29        27       28       59       62 

72  3.078     3.108     3.140       3.172       3.204     3.237     3.27117  32  1    2.7     2.8     5.9     6.2 

73  3.271     3.305     3.340       3.376       3.412     3.450     3.487  16  36  2    5.4     5.6  11.8  12.4 

74  3.487     3.526     3.566       3.606       3.647     3.689     3.732  15  41  3    8.1     8.4  17.7  18.6 

4  10.8  11.2  23.6  24.8 

75  3.732     3.776     3.821       3.867       3.9M     3.962     4.01114  46  5  13.5  14.0  29.5  31.0 

76  4.011     4.061     4.113       4.165       4.219     4.275     4.33113  53  6  16.2  16.8  35.4  37.2 

77  4.331     4.390     4.449       4.511       4.574     4.638.4.705  12  62  7  18.9  19.6  41.3  43.4 

78  4.705     4.773     4.843       4.915       4.989     5.066     5.145  1173  8  21.6  22.4  47.2  49.6 

79  5.145     5.226     5.309       5.396       5.485     5.576     5.67110  88  9  24.3  25.2  53.155.8 

80  5.671  5.769     5.871  5.976  6.084     6.197     6.314  9              64       67       68       70 

81  6.314  6.435     6.561  6.691  6.827     6.968     7.115  8  1    6.4     6.7     6.8     7.0 

82  7.115  7.269     7.429  7.596  7.770     7.953     8.144  7  2  12.8  13.4  13.6  14.0 

83  8.144  8.345     8.556  8.777  9.010     9.255     9.514  6  3  19.220.120.421.0 

84  9.514  9.788  10.078  10.385  10.712  11.059  11.430  5  4  25.6  26.8  27.2  28.0 

532.0  33.5  34.0  35.0 

85  11.430  11.826  12.251     12.706     13.197  13.727  14.301     4         638.4  40.2  40.8  42.0 

86  14.30114.924  15.605     16.350     17.169  18.075  19.081     3         7  44.8  46.9  47.6  49.0 

87  19.081  20.206  21.470     22.904     24.542  26.432  28.636     2         8  51.2  53.6  54.4  56.0 

88  28.636  31.242  34.368     38.188     42.964  49.104  57.290     1         9  57.660.361.263.0 

89  57.290  68.750  85.940     114.59     171.89  343.77  infinit      0 

60'  50'  40'  30'  20'  10'  0'      A°  d.  P.  P. 

NUMERICAL  VALUES  OF  COTANGENTS 


—  23  — 


TABLE  IX 


SQUii 

dlES,  CUBES, 

SQUARE  ROOTS,  CUBE  ROOTS, 

RECIPROCALS, 

1-100 

n   n2 

n3 

Vn 

^n 

1/n 

n 

n2 

n3 

Vn 

^n 

1/n 

1       1 

1 

1.0000 

1.0000  1.00000 

51 

2601 

132651 

7.1414 

3.7084 

.01961 

2        4 

8 

1.4142 

1.2599 

.50000 

52 

2704 

140608 

7.2111 

3.7325 

.01923 

3        9 

27 

1.7321 

1.4422 

.33333 

53 

2809 

148877 

7.2801 

3.7563 

.01887 

4       16 

64 

2.0000 

1.5874 

.25000 

54 

2916 

157464 

7.3485 

3.7798 

.01852 

5      25 

125 

2.2361 

1.7100 

.20000 

55 

3025 

166375 

7.4162 

3.8030 

.01818 

6      36 

216 

2.4495 

1.8171 

. 16667 

56 

3136 

175616 

7.4833 

3.8259 

.01786 

7      49 

343 

2.6458 

1.9129 

. 14288 

57 

3249 

185193 

7.5498 

3 . 8485 

.01754 

8      64 

512 

2.8284 

2.0000 

. 12500 

58 

3364 

195112 

7.6158 

3.8709 

.01724 

9      81 

729 

3.0000 

2.0801 

.11111 

59 

3481 

205379 

7.6811 

3.8930 

.01695 

10    100 

1000 

3.1623 

2.1544 

. 10000 

60 

3600 

216000 

7.7460 

3.9149 

.01667 

11    121 

1331 

3.3166 

2.2240 

.09091 

61 

3721 

226981 

7.8102 

3.9365 

.0l6a9 

12    144 

1728 

3.4641 

2.2894 

.08.333 

62 

3844 

238328 

7.8740 

3.9579 

.01613 

13    169 

2197 

3 . 6056 

2.3513 

. 07692 

63 

3969 

250047 

7.9373 

3.9791 

.01587 

14    196 

2744 

3.7417 

2.4101 

.07143 

64 

4096 

262144 

8.0000 

4.0000 

.01563 

15    225 

3375 

3.8730 

2.4662 

.06666 

65 

4225 

274625 

8.0623 

4.0207 

.01538 

16    256 

4096 

4.0000 

2.5198 

.06250 

66 

4356 

287496 

8.1240 

4.0412 

.01515 

17    289 

4913 

4.1231 

2.5713 

.05882 

67 

4489 

300763 

8.1854 

4.0615 

.0149  J 

18    324 

5832 

4.2426 

2.6207 

.05556 

68 

4624 

314432 

8.2462 

4.0817 

.01471 

19    361 

6859 

4.3589 

2.6684 

.05263 

69 

4761 

328509 

8.3066 

4.1016 

.01449 

20    400 

8000 

4.4721 

2.7144 

.05000 

70 

4900 

343000 

8.3666 

4.1213 

.01429 

21    441 

9261 

4 . 5826 

2.7589 

.04762 

71 

5041 

357911 

8.4261 

4.1408 

.01408 

22    484 

10648 

4.6904 

2.8020 

.04545 

72 

5184 

373248 

8.4853 

4 . 1602 

.01389 

23    529 

12167 

4.7958 

2.8439 

.04348 

73 

5329 

389017 

8.5440 

4.1793 

.01370 

24    576 

13824 

4.8990 

2.8845 

.04167 

74 

5476 

405224 

8.6023 

4.1983 

.01351 

n   n2 

n3 

Vn 

^n 

1/n 

n 

n2 

n3 

Vn 

^n 

1/n 

25    625 

15625 

5.0000 

2.9240 

.04000 

75 

5625 

421875 

8.6603 

4.2172 

.01333 

26    676 

17576 

5.0990 

2.9625 

.03846 

76 

5776 

438976 

8.7178 

4.2358 

.01316 

27    729 

19683 

5.1962 

3.0000 

.03704 

77 

5929 

456533 

8.7750 

4.2.543 

.01299 

28    784 

21952 

5.2915 

3.0366 

.03571 

78 

6084 

474552 

8.8318 

4.2727 

.01282 

29    841 

24389 

5.3852 

3.0723 

.03448 

79 

6241 

493039 

8.8882 

4.2908 

.01266 

30    900 

27000 

5.4772 

3.1072 

.03333 

80 

6400 

512000 

8.9443 

4.3089 

.01250 

31    961 

29791 

5.5678 

3.1414 

.03226 

81 

6.561 

531441 

9.0000 

4.3267 

.01235 

32  1024 

32768 

5.6569 

3.1748 

.03125 

82 

6724 

551368 

9 . 0554 

4.3445 

.01220 

33  1089 

35937 

5.7446 

3.2075 

.03030 

83 

6889 

571787 

9.1104 

4.3621 

.01205 

34  1156 

39304 

5.8310 

3.2396 

.02941 

84 

7056 

592704 

9.1652 

4.3795 

.01190 

35  1225 

42875 

5.9161 

3.2711 

.02857 

85 

7225 

614125 

9.2195 

4.3968 

.01176 

36  1296 

46656 

6.0000 

3.3019 

.02778 

86 

7396 

636056 

9.2736 

4.4140 

.01163 

37  1369 

50653 

6.0828 

3.3322 

.02703 

87 

7569 

658503 

9.3274 

4.4310 

.01149 

38  1444 

54872 

6.1644 

3.3620 

.02632 

88 

7744 

681472 

9.3808 

4.4480 

.01136 

39  1521 

59319 

6.2450 

3.3912 

.02564 

89 

7921 

704969 

9.4340 

4.4647 

.01124 

40  1600 

64000 

6.3246 

3.4200 

.02500 

90 

8100 

729000 

9.4868 

4.4814 

.01111 

41  1681 

68921 

6.4031 

3.4482 

.02439 

91 

8281 

753571 

9.5.94 

4.4979 

.01099 

42  1764 

74088 

6.4807 

3.4760 

.02381 

92 

8464 

778688 

9.5917 

4.5144 

.01087 

43  1849 

79507 

6 . 5574 

3.5034 

.0232(3 

93 

8649 

804357 

9.6437 

4.5307 

.01075 

44  1936 

85184 

6.6332 

3.5303 

.02273 

94 

8836 

830584 

9.6954 

4.5468 

.01064 

45  2025 

91125 

6.7082 

3 . 5569 

.02222 

95 

9025 

857375 

9.7468 

4.5629 

.01053 

46  2116 

97336 

6.7823 

3.5830 

.02174 

96 

9216 

884736 

9.7980 

4.5789 

.01042 

47  2209  103823 

6.8557 

3.6088 

.02128 

97 

9409 

912673 

9.8489 

4.5917 

.01031 

48  2304  110592 

6.9282 

3.6342 

.02083 

98 

9604 

911192 
970299 

9.8995 

4.6104 

.01020 

49  2401  117649 

7.0000 

3.6593 

.02041 

99 

9801 

9.9499 

4.6261 

.01010 

50  2500  125000 

7.0711 

3.6840 

.02000  ; 

100  10000 

1000000 

10.0000 

4.6416 

.01000 

n   n^ 

n3 

Vn 

^n 

1/n 

n 

n2 

n3 

Vn 

Vn 

1/n 

TABLE  X 


Degrees 

t  to  radians 

Minutes 

Radians  to  De- 

10° 0.17453 

60° 1.04720 

10' 0.00291: 

^rees 

and  minutes 

Power  Function 

H°0. 19199 

61°  1.06465 

11' 0.00320 

1 

57°17'45" 

X 

EX         E-" 

12°  0.20944 

62°  1.08210 

12-0.00349 

2 

114°35'30" 

0.0 

1.0000  1.0000 

13°  0.22689 

63°  1.09956 

13*0.00378 

3 

171°53'14" 

0.1 

1.1052  0.9048 

14  °  0 .  24435 

64°  1.11701 

14-0.00407 

4 

229°10'59" 

0.2 

1.2214  0.8187 

15°  0.26180 

65°  1.13446 

15*0.00436 

5 

286°28'44" 

0.3 

1.3499  0.7408 

16°  0.27925 

66°  1.15192 

16' 0.00465 

6 

343°46'29" 

0.4 

1.4918  0.6703 

17°  0.29671 

67° 1.16937 

17-0.00495 

7 

401°  4'14" 

0.5 

1.6487  0.6065 

18°  0.31416 

68°  1.18682 

18-0.00524 

8 

458°21'58" 

0.6 

1.8221  0.5488 

19°0. 33161 

69°  1.20428 

19-0.00553 

9 

515°39'43" 

0.7 
0.8 

2.0138  0.4966 
2.2255  0.4493 

20°  0.34907 

70°  1.22173 

20-0.00582 

.1 

5°43'47" 

0.9 

2.4596  0.4066 

21° 0.36652 

71°  1.23918 

21-0.00611 

.2 

11°27'33" 

1.0 

2.7183  0.3679 

22°  0.38397 

72°  1.25664 

22-0.00640 

.3 

17°11'19" 

1.1 

3.0042  0.3329 

23°  0.40143 

73°  1.27409 

23-0.00669 

.4 

22°55'06" 

1.2 

3.3201  0.3012 

24°  0.41888 

74°  1.29154 

24-0.00698 

.5 

28°38'52" 

1.3 

3.6693  0.2725 

25°  0.43633 

75°  1.30900 

25-0.00727 

.6 

34°22'39" 

1.4 

4.0552  0.2466 

26°  0.45379 

76°  1.32645 

26-0.00756 

.7 

40°  6'25" 

1.5 

4.4817  0.2231 

27°  0.47124 

77°  1.34390 

27-0.00785 

.8 

45°50'12" 

1.6 

4.9530  0.2019 

28° 0.48869 

78°  1.36136 

28-0.00814 

.9 

51  °33'58" 

1.7 

5.4739  0.1827 

29°  0.50615 

79°  1.37881 

29' 0.00844 

1.8 

6.0496  0.1653 

.01 

0°34'23" 

1.9 

6.6859  0.1496 

30°  0.52360 

80° 1.39626 

30-0.00873 

.02 

1°  8'45" 

31°  0.54105 

81°  1.41372 

31-0.00902 

.03 

1  °43'08" 

2.0 

7.3891  0.1353 

32  "0.55851 

82°  1.43117 

32-0.00931 

.04 

2°17'31" 

2.1 

8.1662  0.1225 

33° 0.57596 

83°  1.44862 

33-0.00960 

.05 

2°51'53" 

2.2 

9.0250  0.1108 

34° 0.59341 

84° 1.46608 

34-0.00989 

.06 

3°20'16" 

2.3 

9.9742  0.1003 

35° 0.01087 

85°  1.48353 

35-0.01018 

.07 

4°  0'39" 

2.4 

11.023     0.0907 

36° 0.62832 

86°  1.50098 

36-0.01047 

.08 

4°35'01" 

37° 0.64577 

87°  1.51844 

37-0.01076 

.09 

5°  9 '24" 

2.5 

12.182     0.0821 

38° 0.66323 

88° 1.53589 

38-0.01105 

2.6 

13.464     0.0743 

39° 0.68068 

89° 1.55334 

39-0.01134 

.001 

0°  3'26" 

2.7 

14.880     0.0672 

.002 

0°  6'52" 

2.8 

16.445     0.0608 

40°  0.69813 

90° 1.57080 

40-0.01164 

.003 

0°10'18" 

2.9 

18.174     0.0550 

41°  0.71559 

91°  1.58825 

41-0.01193 

.004 

0°13'45" 

42°  0.73304 

92° 1.60570 

42-0.01222 

.005 

0°17'11" 

3.0 

20.086        .0498 

43°  0.75049 

93°  1.62316 

43-0.01251 

.006 

0°20'37" 

3.0 

33.115        .0302 

44°  0.76794 

94° 1.64061 

44-0.01280 

.007 

0°24'03" 

4.0 

54.598        .0183 

45°  0.78540 

95° 1.65806 

45-0.01309 

.008 

0°27'30" 

5.0 

148.41          .0067 

46°  0.80285 

96° 1.67552 

46-0.01338 

.009 

0°30'56" 

6.0 

403.4            .00248 

47°  0.82030 

97°  1.69297 

47-0.01367 

7.0 

1097                .00091 

48°  0.83776 

98° 1.71042 

48-0.01396 

8.0 

2981                 .00034 

49°  0.85521 

99° 1.72788 

49' 0.01425 

9.0 
10.0 

8103                .00012 
22000              .00005 

50°  0.87266 

100° 1.74533 

50-0.01454 

51°  0.89012 

101° 1.76278 

51-0.01484 

Degrees  and  Minutes  to  Radians 

52°  0.90757 

102°  1.78024 

52-0.01513 

1°=. 01745 

1'  =  . 00029 

53°  0.92502 

103°  1.79769 

53' 0.01542 

2°=  .03491 

2' =  .00058 

54°  0.94248 

104°  1.81514 

54-0.01571 

3°= .05236 

3' =  .00087 

55°  0.95993 

105°  1.83260 

55-0.01600 

4°  =.06981 

4' =.001 16 

56°  0.97738 

103°  1.85005 

56-0.01629 

5°=.  .08728 

5' =.00145 

57°  0.99481 

107°  1   86750 

57-0.01658 

6°=.  10472 

6' =.00175 

58°  1.01229 

103°  1.88496 

58-0.01687 

7°=. 12217 

7'=  .00204 

59°  1.20974 

109°  1.90241 

59-0.01716 

8°  =.13963 

8'=,  .00233 

60° 1.04720 

110° 1.91986 

60' 0.01745 

9°=.  15708 

9  = .00262 

—  25  — 


TABLE  XI 


ACCUMULATION  OF  1  AT  THE  END  OF  n  YEARS 


Yrs. 

.    VA% 

2% 

2yz7c 

3% 

4% 

5% 

6%     Yrs. 

1 

1.01500 

1.02000 

1.02500 

1.03000 

1.04000 

1.05000 

1.06000 

1 

2 

1.03023 

1.04040 

1.05063 

1.06090 

1.08160 

1 . 10250 

1.12360 

2 

3 

1.04568 

1.06121 

1.07689 

1.09273 

1 . 12486 

1.15763 

1.19102 

3 

4 

1.06136 

1.08243 

1 . 1038 

1.12551 

1 . 16986 

1.21551 

1.26248 

4 

5 

1.07728 

1 . 10408 

1.13141 

1 . 15927 

1.21665 

1.27628 

1.33823 

5 

6 

1.09344 

1.12616 

1.15969 

1 .  19405 

1.26532 

1.34010 

1.41852 

6 

7 

1 . 10984 

1 . 14869 

1.18869 

1.22987 

1.31593 

1.40710 

1.50363 

7 

8 

1.12649 

1.17166 

1.21840 

1.26677 

1.36857 

1.47746 

1.59385 

8 

9 

1 . 14339 

1 . 19509 

1.24886 

1.30477 

1.42331 

1.55133 

1.68948 

9 

10 

1 . 16054 

1.21900 

1.28008 

1.34392 

1.48024 

1.62890 

1.79085 

10 

11 

1.17795 

1.24337 

1.31209 

1.38423 

1 . 53945 

1.71034 

1.89831 

11 

12 

1 . 19562 

1.26824 

1.34489 

1.42576 

1.60103 

1.79586 

2.01220 

12 

13 

1.21355 

1.29361 

1.37851 

1.46853 

1.66507 

1.88565 

2 . 13293 

13 

14 

1.23176 

1.31948 

1.41297 

1.51259 

1.73168 

1.97993 

2.26090 

14 

15 

1.25023 

1.34587 

1.44830 

1.55797 

1.80094 

2.07893 

2.39656 

15 

16 

1.26899 

1.37279 

1.48451 

1.60471 

1.87298 

2.18287 

2.54035 

16 

17 

1.28802 

1.40024 

1.52162 

1.65285 

1.94730 

2.29202 

2.69277 

17 

18 

1.30734 

1.42825 

1.55966 

1.70243 

2.02582 

2.40662 

2.85434 

18 

19 

1.32695 

1.45681 

1.59865 

1.75351 

2.10685 

2.52695 

3.02560 

19 

20 

1.34686 

1.48595 

1.63862 

1.80611 

2.19112 

2.65330 

3.20714 

20 

Yrs. 

13^% 

2% 

2y2% 

3% 

4% 

5% 

6%       Yrs. 

21 

1.36706 

1.51567 

1.67958 

1.86029 

2.27877 

2.78596 

3.39956 

21 

22 

1.38756 

1.54598 

1.72157 

1.91610 

2.36992 

2.92526 

3.60354 

22 

23 

1.40838 

1.57690 

1.76461 

1.97359 

2.46472 

3.07152 

3.81975 

23 

24 

1.42950 

1.60844 

1.80873 

2.03279 

2.56330 

3.22510 

4.04893 

24 

25 

1.45095 

1.64061 

1.85394 

2.09378 

2.66584 

3.38635 

4.29187 

25 

26 

1.47271 

1.67342 

1.90029 

2.15659 

2.77247 

3.55567 

4.54938 

26 

27 

1.49480 

1 . 70689 

1.94780 

2.22129 

2.88337 

3.73346 

4.82235 

27 

28 

1.51722 

1.74102 

1.99650 

2.28793 

2.99870 

3.92013 

5.11169 

28 

29 

1 . 53998 

1.77584 

2.04641 

2.35657 

3.11865 

4.11614 

5.41839 

29 

30 

1.56308 

1.81136 

2.09757 

2.42726 

3.2434 

4.32194 

5.74349 

30 

31 

1.58653 

1.84759 

2.15001 

2.50008 

3.37313 

4.53804 

6.08810 

31 

32 

1.61032 

1.88454 

2.20376 

2.57508 

3.50806 

4.76494 

6.45339 

32 

33 

1.63448 

1.92223 

2.25885 

2.65234 

3.64838 

5.00319 

6.84059 

33 

34 

1.65900 

1.96068 

2.31532 

2.73191 

3.79432 

5.25335 

7.25103 

34 

35 

1.68388 

1.99989 

2.37321 

2.81386 

3.94609 

5.51602 

7.68609 

35 

36 

1.70914 

2.03989 

2.43254 

2.89828 

4.10393 

5.79182 

8.14725 

36 

37 

1.73478 

2.08069 

2.49335 

2.98523 

4.26809 

6.08141 

8.63609 

37 

38 

1.76080 

2.12230 

2.55568 

3.07478 

4.43881 

6.38548 

9.15425 

38 

39 

1.78721 

2.16474 

2.61957 

3.16703 

4.61637 

6.70475 

9.70351 

39 

40 

1.81402 

2.20804 

2.68506 

3.26204 

4.80102 

7.03999 

10.28572 

40 

50 

2.10524 

2.69159 

3.43711 

4.38391 

7.10668 

11.46740 

18.42015 

50 

60 

2.44322 

3.28103 

4.39979 

5.89160 

10.51963 

18.67919 

32.98769 

60 

70 

2.83546 

3.99956 

5.63210 

7.91782 

15.57162 

30.42643 

59.07593 

70 

80 

3.29066 

4.87544 

7.20957 

10.64089 

23.04980 

49.56144 

105.79599 

80 

90 

3.81895 

5.94313 

9.22886 

14.30047 

34.11933 

80.73037 

189.46450 

90 

100 

4.43205 

7.24465 

11.81372 

19.21863 

50.50495 

131.50126 

339.30208 

100 

Yrs. 

1M% 

2% 

2H% 

3% 

4% 

5% 

6%       Yrs. 

—   26   — 


TABLE  XII 


THE  PRESENT  VALUE  OF  1  DUE  IN  n  YEARS 


Yrs, 

.  VA%. 

2%. 

2^%. 

3%. 

4%. 

5%. 

6%.  Yrs. 

1 

0.98522 

0.98039 

0.97561 

0.97087 

0.96154 

0.95238 

0.94340  1 

2 

0.97066 

0.96117 

0.95181 

0.94260 

0.92456 

0.90703 

0.89000  2 

3 

0.95632 

0.94232 

0.92860 

0.91514 

0.88900 

0.86384 

0.83962  3 

4 

0.94218 

0.92.385 

0.90595 

0 . 88849 

0.85480 

0.82270 

0.79209  4 

5 

0.92826 

0.90573 

0.88385 

0.86261 

0.82193 

0.78353 

0.74726  5 

6 

0.91454 

0.88797 

0.86230 

0.83748 

0.79031 

0.74622 

0.70496  6 

7 

0.90103 

0.87056 

0.84127 

0.81309 

0.7.5992 

0.71068 

0.66.506  7 

8 

0.88771 

0.85349 

0.82075 

0.78941 

0.73069 

0.67684 

0.62741  8 

9 

0.87459 

0.83676 

0.80073 

0.76642 

0.70259 

0.64461 

0.59190  9 

10 

0.86167 

0.82035 

0.78120 

.0.74409 

0.67556 

0.61391 

0.55839  10 

11 

0.84893 

0.80426 

0.76214 

0.72242 

0.64958 

0.58468 

0.52679  11 

12 

0.83639 

0.78849 

0.74356 

0.70138 

0.62460 

0.55684 

0.49697  12 

13 

0.82403 

0.77303 

0.72542 

0.68095 

0.60057 

0.53032 

0.46884  13 

14 

0.81185 

0.7.5788 

0.70773 

0.66112 

0.57748 

0.50507 

0.442.30  14 

15 

0.79985 

0.74301 

0.69047 

0.64186 

0.55526 

0.48102 

0.41727  15 

16 

0.78803 

0.72845 

0.67362 

0.62317 

0.53391 

0.45811 

0.39365  16 

17 

0.77639 

0.71416 

0.65720 

0.60502 

0.51337 

0.43630 

0.37136  17 

18 

0.76491 

0.70016 

0.64117 

0.58739 

0.49363 

0.41552 

0.35034  18 

19 

0.75361 

0.68643 

0.62553 

0.57029 

0.47464 

0.39573 

0.33051  19 

20 

0.74247 

0.67297 

0.61027 

0.55368 

0.45639 

0.37689 

0.31180  20 

Vrs. 

1M%. 

2%. 

23^%. 

3%. 

4%. 

5%. 

6%.  Yrs. 

21 

0.73150 

0.65978 

0 . 59539 

0.53755 

0.43883 

0.35894 

0.29416  21 

22 

0.72069 

0.64684 

0.58086 

0.52189 

0.42196 

0.34185 

0.27751  22 

23 

0.71004 

0.63416 

0.56670 

0.50669 

0.40573 

0.325.57 

0.26180  23 

24 

0.69954 

0.62172 

0.55288 

0.49193 

0.39012 

0.31007 

0.24698  24 

25 

0.68921 

0.60953 

0.53939 

0.47761 

0.37512 

0.29530 

0.23300  25 

26 

0.67902 

0.59758 

0.52623 

0.46369 

0.36069 

0.28124 

0.21981  26 

27 

0.66899 

0.58586 

0.51340 

0.45019 

0.34682 

0.26785 

0.20737  27 

28 

0.65910 

0.57437 

0.50088 

0.43708 

0.33348 

0.25509 

0.19563  28 

29 

0.64936 

0.56311 

0.48866 

0.42435 

0.32065 

0.24295 

0.18456  29 

30 

0.63976 

0.55207 

0.47674 

0.41199 

0.30832 

0.23138 

0.17411  30 

31 

0.63031 

0.54125 

0.46511 

0.39999 

0.29646 

0.22036 

0.16425  31 

32 

0.62099 

0.53063 

0.45377 

0.38834 

0.28506 

0.20987 

0.15496  32 

33 

0.61182 

0.52023 

0.44270 

0.37703 

0.27409 

0.19987 

0.14619  33 

34 

0.60277 

0.51003 

0.43191 

0.36604 

0.26355 

0.19035 

0.13791  34 

35 

0.59387 

0.50003 

0.42137 

0.35538 

0.25342 

0.18129 

0.13011  35 

36 

0.58509 

0.49022 

0.41109 

0.34503 

0.24367 

0.17266 

0.12274  36 

37 

0.57644 

0.48061 

0.40107 

0.33498 

0.23430 

0.16444 

0.11579  37 

38 

0.56792 

0.47119 

0.39128 

0.32523 

0.22529 

0.15661 

0.10924  38 

39 

0.55953 

0.46195 

0.38174 

0.31575 

0.21662 

0.14915 

0.10306  39 

40 

0.55126 

0.45289 

0.37243 

0.30656 

0.20829 

0.14205 

0.09722  40 

50 

0.47500 

0.37153 

0.29094 

0.22811 

0.14071 

0.08720 

0.05429  50 

60 

0.40930 

0.30478 

0.22728 

0.16973 

0.09506 

0.05354 

0.03031  60 

70 

0.35268 

0.25003 

0.17755 

0.12630 

0.06422 

0.03287 

0.01693  70 

80 

0.30389 

0.20511 

0.13870 

0.09398 

0.04338 

0.02018 

0.00945  80 

90 

0.26185 

0.16826 

0.10836 

0.06993 

0.02931 

0.01239 

0.00527  90 

100 

0.22563 

0.13803 

0.08465 

0.05203 

0.01980 

0.00760 

0.00295100 

frs. 

1^%. 

2%. 

2K%. 

3%. 

4%. 

5%. 

6%.  Yrs. 

—    27    — 


TABLE  XIII 


THE  ACCUMULATION  OF  AN  ANNUITY    OF    1   PER   ANNUM   AT   THE   END 


OF  n  YEARS 

Yrs 

.  13^%. 

2%. 

2H%. 

3%. 

4%. 

5%. 

6%.  Yrs. 

1 

1.00000 

1.00000 

1.00000 

1.00000 

1  00000 

1.00000 

1.00000  1 

2 

2.01500 

2.02000 

2.02500 

2.03000 

2.04000 

z. 05000 

2.06000  2 

3 

3.04523 

3.06049 

3.07563 

3.09090 

3.12160 

3.15250 

3 .  18360  3 

4 

4.09090 

4.12161 

4.15252 

4.18363 

4.24646 

4.31013 

4.37467  4 

5 

5.15227 

5.20404 

5.25633 

5.30914 

5.41632 

5.52563 

5.63709  5 

6 

6.22955 

6.30812 

6.38774 

6.46841 

6.63298 

6.80191 

6.97532  6 

7 

7.32299 

7.43428 

7.54743 

7.66246 

7.89829 

8.14201 

8.39384  7 

8 

8.43284 

8 . 58297 

8.73612 

8 . 89234 

9.21423 

9.54911 

9.89747  8 

9 

9.55933 

9.75463 

9.95452 

10.15911 

10.58280 

11.02656 

11.49132  9 

10 

10.70272 

10.94972 

11.20338 

11.46388 

12.00611 

12 . 57789 

13.18080  10 

11 

11.8G326 

12.16872 

12.48347 

12.80780 

13.48635 

14.20679 

14.97164  11 

12 

13.04121 

13.41209 

13.79555 

14. 19202 

15.02581 

15.91713 

16.86994  12 

13 

14.23683 

14.68033 

15.14044 

15.61779 

16.62684 

17.71298 

18.88214  13 

14 

15.45038 

15.97394 

16.51895 

17.08632 

18.29191 

19.59863 

21.01507  14 

15 

16.68214 

17.29342 

17.93193 

18.59891 

20.02359 

21.57856 

23.27597  15 

IS 

17.93237 

18.63929 

19 . 38022 

20.15688 

21.82453 

23.65749 

25.67255  16 

17 

19.20136 

20.01207 

20.86473 

21.76159 

23.69751 

25.84037 

28.21288  17 

18 

20.48938 

21.41231 

22.38635 

23.41444 

25.64541 

28.13238 

30.90565  18 

19 

21.79672 

22.84056 

23.94601 

25.11687 

27.67123 

30.53900 

33.75999  19 

20 

23.12367 

24.29737 

25.54466 

26.87037 

29.77808 

33.06595 

36.78559  20 

Yrs. 

VA%. 

2%. 

2y2%. 

3%. 

4%. 

5%. 

6%.   Yrs. 

21 

24.47052 

25.78332 

27.18327 

28.67649 

31.96920 

35.71925 

39.99273  21 

22 

25.83758 

27.29898 

28.86286 

30.53678 

34.24797 

38.50521 

43.39229  22 

23 

27.22514 

28.84496 

30.58443 

32.45288 

36.61789 

41.43048 

46.99583  23 

24 

28.63352 

30.42186 

32 . 34904 

34.42647 

39.08260 

44.50200 

50.81558  24 

25 

30.06302 

32.03030 

34.15776 

36.45926 

41.64591 

47.72710 

54.86451  25 

26 

31.51397 

33.67091 

36.01171 

38.55304 

44.31174 

51.11345 

59.15638  26 

27 

32.986G8 

35.34432 

37.91200 

40.70963 

47.08421 

54.66913 

63.70577  27 

28 

34.48148 

37.05121 

39.85980 

42.93092 

49.96758 

58.40258 

68.52811  28 

29 

35.99870 

38.79223 

41.85630 

45.21885 

52.96629 

62.32271 

73.63980  29 

30 

37.53868 

40.56808 

43.90270 

47.57542 

56.08494 

66.43885 

79.05819  30 

31 

39.10176 

42.37944 

46.00027 

50.00268 

59.32834 

70.76079 

84.80168  31 

32 

40.68829 

44.22703 

48.15028 

52 . 50276 

62.70147 

75.29883 

90.88978  32 

33 

42.29861 

46.11157 

50.35403 

55.07784 

66.20953 

80.06377 

97.34316  33 

34 

43.93309 

48.03380 

52.61289 

57.73018 

69.85791 

85.06696 

104.18375  34 

35 

45 . 59209 

49.99448 

54.92821 

60.46208 

73.65222 

90.32031 

111.43478  35 

36 

47.27597 

51.99437 

57.30141 

63.27594 

77.59831 

95.83632 

119.12087  36 

37 

48.98511 

54.03425 

59.73395 

66.17422 

81.70225 

101.62814 

127.26812  37 

38 

50.71989 

56.11494 

62.22730 

69.15945 

85.97034 

107.70955 

135.90421  38 

39 

52.48068 

58.23724 

64.78298 

72.23423 

90.40915 

114.09502 

145.05846  39 

40 

54.26789 

60.40198 

67.40255 

75.40126 

95.02552 

120.79977 

154.76197  40 

50 

73.68283 

84.57940 

97.48433 

112.79686 

152.66703 

209.34800 

290.33590  50 

CO 

96.21465 

114.05154 

135.99159 

163.05344 

237.99069 

353.58372 

533.12818  60 

70 

122.36375 

149.97791 

185.28411 

230.59406 

364.29046 

588.52851 

967.93216  70 

00 

152. 7108  ■) 

193.77195 

248.38271 

321.36302 

551.24498 

971.22882 

1746.59989  80 

90 

187. 9299 J 

247.15666 

329.15425 

443.34890 

827.98333 

1594.60730 

3141.07519  90 

100  22S. 80304 

312.23230 

432,54865 

607.28773 

1237.62370  : 

2610.02516 

5638.36805100 

Yrs. 

1>^%. 

2%. 

2y2%. 

3%. 

4%. 

5%. 

6%.   Yrs. 

—  28  — 


TABLE  XIV 


THE  PRESENT  VALUE  OF  AN  ANNUITY  OF  1  FOR  n  YEARS 


Yrs.  1'2%. 

2^. 

214^. 

3%. 

4%. 

5%. 

6%.  Yrs. 

1  0.98.522 

0.98039 

0.97561 

0.97087 

0.96154 

0.95238 

0.94340  1 

2  1 .95588 

1.94156 

1.92742 

1.91347 

1.88609 

1.85941 

1.83339  2 

3  2.91220 

2.88388 

2.8.1002 

2.82861 

2.77.509 

2.72325 

2.67301  3 

4  3.85438 

3.80773 

3.76197 

3.71710 

3.62990 

3.54595 

3.46511  4 

5  4.78265 

4.71346 

4.64583 

4.57971 

4.45182 

4.32948 

4.21236  5 

6  5.69719 

5.60143 

5.50813 

5.41719 

5.24214 

5.07569 

4.91732  6 

7  6.59821 

6.47199 

6.34939 

6.23028 

6.00205 

5.78637 

5.58238  7 

8  7.48593 

7.32548 

7.17014 

7.01969 

6.73274 

6.46321 

6.20979  8 

9  8 . 36052 

8.16224 

7.97087 

7.78611 

7.43533 

7 . 10782 

6.80169  9 

10  9.22218 

8.98259 

8.75206 

8.53020 

8.11090 

7.72173 

7.36009  10 

11  10.07112 

9.78685 

9.51421 

9.25262 

8.76048 

8.30641 

7.88687  11 

12  10.90751 

10.57534 

10.25776 

9.95400 

9.38507 

8.86325 

8.38384  12 

13  11.73153 

11.34837 

10.98319 

10.63496 

9.98565 

9.39357 

8.85208  13 

14  12.54338 

12.10625 

11.69091 

11.29607 

10.56312 

9.89864 

9.29498  14 

15  13.34323 

12.84926 

12.38138 

11.93794 

11.11839 

10.37966 

9.71225  15 

16  14.13126 

13.57771 

13.05500 

12.56110 

11.65230 

10.83VVV 

10.10.590  16 

17  14.90765 

14.29187 

13.71220 

13.16612 

12.16567 

11.27407 

10.47726  17 

18  15.67256 

14.99203 

14.. 3.53.36 

13.75351 

12.65930 

11.68959 

10.82760  18 

19  16.42617 

15.67846 

14.97889 

14.32380 

13.13394 

12.08532 

11.15812  19 

20  17.16864 

16.35143 

15.58916 

14.87747 

13.59033 

12.46221 

11.46992  20 

Yrs.  11^%. 

2%. 

2J^%. 

3%. 

4%. 

5%. 

6%.  Yrs. 

21  17.90014 

17.01121 

16.184.55 

15.41502 

14.02916 

12.82115 

11.76408  21 

22  18.f2082 

17.65805 

16.76541 

15.93692 

14.45112 

13 . 16300 

12.04158  22 

23  19.33080 

18.29220 

17.. 33211 

16.44361 

14.85684 

13.48857 

12.. 30338  23 

24  20.03041 

18.91393 

17.88499 

16.93554 

15.24696 

13.79864 

12.. 5.5036  24 

25  20.71961 

19.52346 

18.42438 

17.41315 

15.62208 

14.09394 

12.78336  25 

26  21.39863 

20.12104 

18.95061 

17.87684 

15.98277 

14.37519 

13.00317  26 

27  22.06762 

20.70690 

19.46401 

18.32703 

16.32959 

14.64303 

13.21053  27 

28  22.72672 

21.28127 

19.96489 

18.76411 

16.66306 

14.89813 

13.40016  28 

29  23.37608 

21.84438 

20.45355 

19 . 18845 

16.98371 

15.14017 

13.59072  29 

30  24.01584 

22.39646 

20.93029 

19.60044 

17.29203 

15.37245 

13.76483  30 

31  24.64615 

22.93770 

21.39541 

20.00043 

17.58849 

15.59281 

13.92909  31 

32  25.26714 

23.46833 

21.84918 

20.38877 

17.87355 

15.80268 

14.08404  32 

33  25.87895 

23.98856 

22.29188 

20.76579 

18.14765 

16.00255 

14.23023  33 

34  26.48173 

24.49859 

22.72379 

21.13184 

18.41120 

16 . 19290 

14.36814  34 

35  27.07559 

24.99862 

23.14516 

21.48722 

18.66461 

16.37419 

14.49825  35 

36  27.66068 

25.48884 

23.55625 

21.83225 

18.90828 

16.54685 

14.62099  36 

37  28.23713 

25.96945 

23.95732 

22.16724 

19.14258 

16.71129 

14.73678  37 

38  28.80505 

26.44064 

24.34860 

22.49246 

19.36786 

16.86789 

14.84602  38 

39  29.36458 

26.90259 

24.73034 

22.80822 

19.58448 

17.01704 

14.94907  39 

40  29.91585 

27.35548 

25.10278 

23.11477 

19.79277 

17.15909 

15.04630  40 

50  34.99969 

31.42361 

28.36231 

25.72926 

21.48218 

18.25593 

15.76186  SO 

GO  39.38027 

34.76089 

30.90866 

27.67.556 

22.62349 

18.92929 

16.16143  60 

70  43.1.5487 

37.49862 

32.89786 

29.12342 

23.39451 

19.34268 

16.38454  70 

80  46.40732 

39.74451 

34.45182 

30.20076 

23.91539 

19.59646 

16.50913  80 

90  49.20985 

41.58693 

35.06577 

31.00241 

24.26728 

19.75226 

16.57870  90 

190  51.62470 

43.09835 

36.61411 

31.59891 

24.50500 

19.84791 

16.61755100 

Yrs.  1H%. 

2%. 

2>^%. 

3%. 

4%. 

s%. 

6%.  Yrs. 

29 


TABLE  XV 


THE  ANNUAL  SINKING  FUND  TO  ACCUMULATE  TO  1  AT  THE  END  OF  n  YEARS, 
AND,  BY  ADDITION  OF  i,  THE  ANNUITY  WHICH  1  WILL  PURCHASE 


Yrs. 

.     11-^% 

2% 

21/^% 

3% 

4% 

5% 

6%     Yrs. 

1 

1.00000 

1.00000 

1.00000 

1.00000 

1.00000 

1.00000 

1.00000 

1 

2 

0.49628 

0.49505 

0.49383 

0.49261 

0.49020 

0.48780 

0.48544 

2 

3 

0.32838 

0.32675 

0.32514 

0.32353 

0.32035 

0.31721 

0.31411 

3 

4 

0 . 24444 

0.24262 

0.24082 

0.23903 

0.23549 

0.23201 

0.22859 

4 

5 

0.19409 

0.19216 

0.19025 

0.18835 

0.18463 

0.18097 

0.17740 

5 

6 

0.16053 

0.15853 

0.15655 

0.15460 

0.15076 

0.14702 

0.14336 

6 

7 

0.13656 

0.13451 

0.13250 

0.13051 

0.12661 

0.12282 

0.11914 

7 

8 

0.11858 

0.11651 

0.11447 

0.11246 

0.10853 

0.10472 

0.10104 

8 

9 

0.10461 

0.10252 

0.10046- 

0.09843 

0.09449 

0.09069 

0.08702 

9 

10 

0.09343 

0.09133 

0.08926 

0.08723 

0.08329 

0.07950 

0.07587 

10 

11 

0.08429 

0.08218 

0.08011 

0.07808 

0.07415 

0.07039 

0.06679 

11 

12 

0.07668 

0.07456 

0.07249 

0.07046 

0.06655 

0.06283 

0.05928 

12 

13 

0.07024 

0.06812 

0.06605 

0.06403 

0.06014 

0.05646 

0.05296 

13 

14 

0.06472 

0.06260 

0.06054 

0.05853 

0.05467 

0.05102 

0.04758 

14 

15 

0.05994 

0.05783 

0.05577 

0.05377 

0.04994 

0.04634 

0.04296 

15 

16 

0.05577 
0.05208 

0.05365 
0.04997 

0.05160 
0.04793 

0.04961 
0.04595 

0.04582 
0.04220 

0.04227 

0.03895 

16 

17 

0.03870 

0.03544 

17 

18 

0.04881 

0.04670 

0.04467 

0  04271 

0.03899 

0.03555 

0.03236 

18 

19 

0.04588 

0.04378 

0.04176 

0.03981 

0.03614 

0.0.3275 

0.02962 

19 

20 

0.04325 

0.04116 

0.03915 

0.03722 

0.03358 

0.03024 

0.02718 

20 

21 

0.04087 

0.03878 

0.03679 

0.03487 

0.03128 

0.02800 

0.02500 

21 

22 

0.03870 

0.03663 

0.03465 

0.03275 

0.02920 

■    0.02597 

0.02305 

22 

23 

0.03673 

0.03467 

0.03270 

0.03081 

0.02731 

0.02414 

0.02128 

23 

24 

0.03492 

0.03287 

0.03091 

0.02905 

0.02559 

0.02247 

0  01968 

24 

25 

0.03326 

0.03122 

0.02928 

0.02743 

0.02401 

0.02095 

0.01823 

25 

VAVo 

2% 

2H% 

3% 

4% 

5% 

6% 

26 

0.03173 

0.02970 

0.02777 

0.02594 

0.02257 

0.01956 

0.01690 

26 

27 

0.03032 

0.02829 

0.02638 

0.02456 

0.02124 

0.01829 

0.01570 

27 

28 

0.02900 

0.02699 

0.02509 

0.02329 

0.02001 

0.01712 

0.01459 

28 

29 

0.02778 

0.02578 

0.02389 

0.02211 

0.01888 

0.01605 

0.013.58 

29 

30 

0.02664 

0.02465 

0.02278 

0.02102 

0.01783 

0.01505 

0.01265 

30 

31 

0.02557 

0.02360 

0.02174 

0.02000 

0.01686 

0.01413 

0.01179 

31 

32 

0.02458 

0.02261 

0.02077 

0.01905 

0.01595 

0.01328 

0.01100 

32 

33 

0.02364 

0.02169 

0.01986 

0.01816 

0.01510 

0.01249 

0.01027 

33 

34 

0.02276 

0.02082 

0.01901 

0.01732 

0.01431 

0.01176 

0.00960 

34 

35 

0.02193 

0.02000 

0.01821 

0.01654 

0.01358 

0.01107 

0.00897 

35 

36 

0.02115 

0.01923 

0.01745 

0.01580 

0.01289 

0.01043 

0.00839 

36 

37 

0.02041 

0.01851 

0.01674 

0.01511 

0.01224 

0.00984 

0.00786 

37 

38 

0.01972 

0.01782 

0.01607 

0.01446 

0.01163 

0.00928 

0.00736 

38 

39 

0.01905 

0.01717 

0.01544 

0.01384 

0.01106 

0.00876 

0.00689 

39 

40 

0.01842 

0.01656 

0.01484 

0.01326 

0.01052 

0.00828 

0.00646 

40 

50 

0.01357 

0.01182 

0.01026 

0.00887 

0.00655 

0.00477 

0.00344 

50 

60 

0.01039 

0.00877 

0.00735 

0.00613 

0.0042:) 

0.00283 

0.00188 

60 

70 

0.00817 

0.00667 

0.00540 

0.00434 

0.00275 

0.00170 

0.00103 

70 

80 

0.00655 

0.00516 

0.00403 

0.00311 

0.00181 

0.00103 

0.00057 

80 

90 

0.00532 

0.00405 

0.00304 

0.00226 

0.00121 

0.00063 

0.00032 

90 

100 

0.00437 

0.00321 

0.00231 

0.00165 

0  00081 

0.00038 

0.00018 

100 

Yrs. 

iy2% 

2% 

2y2% 

3% 

4% 

5% 

6%    y 

'rs. 

30 


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